[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"skill:01M7CSBP2FNKFJ9TSFDRYHDTZG":3,"skill-same:01M7CSBP2FNKFJ9TSFDRYHDTZG":184},{"skillNo":4,"name":5,"nameZh":6,"description":7,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":16,"categories":17,"keywords":18,"publishedAt":19,"linkOnly":20,"markdownContent":21,"markdownBody":22,"frontMatter":23,"refName":33,"commitSha":34,"skillDirectory":35,"forksCount":36,"repositoryHtmlUrl":37,"repositoryHomepageUrl":38,"ownerHtmlUrl":39,"ownerBlogUrl":6,"ownerDescription":40,"updatedAt":41,"install":42,"resources":55},"01M7CSBP2FNKFJ9TSFDRYHDTZG","cuopt-numerical-optimization-api-python",null,"Solve LP, MILP, QP (beta) with cuOpt Python API — linear\u002Fquadratic objectives, integer variables, scheduling, portfolio, least squares.","YYC-Cube\u002FYYC3-Knowledge-Base","YYC-Cube","https:\u002F\u002Favatars.githubusercontent.com\u002Fu\u002F235006543?v=4","01M79J2PH4SWD2X0825X6PN748","yyc3","01M79J2PHVK3F6ZBYT8K2SCZCW",1,"Apache-2.0","https:\u002F\u002Fgithub.com\u002FYYC-Cube\u002FYYC3-Knowledge-Base\u002Fblob\u002Fmain\u002FYYC3-Skills-技能包\u002FYYC3-Skills-技能包-skills\u002Fskills\u002Fcuopt-numerical-optimization-api-python\u002FSKILL.md",[],[],"2026-11-15 14:19:17",false,"---\nname: cuopt-numerical-optimization-api-python\nversion: \"26.08.00\"\ndescription: Solve LP, MILP, QP (beta) with cuOpt Python API — linear\u002Fquadratic objectives, integer variables, scheduling, portfolio, least squares.\nlicense: Apache-2.0\nmetadata:\n  author: NVIDIA cuOpt Team\n  tags:\n    - cuopt\n    - linear-programming\n    - milp\n    - qp\n    - python\n---\n\n\n# cuOpt Numerical Optimization Skill (Python)\n\nModel and solve LP, MILP, and QP problems using NVIDIA cuOpt's GPU-accelerated solver. The Python API surface (`Problem`, `SolverSettings`, `solve`) is shared across all three problem classes — only the objective form and a few rules change.\n\n## Before You Start\n\nUse a formulation summary (parameters, constraints, decisions, objective) if available; otherwise ask for decision variables, objective, and constraints. Then confirm **problem type** (LP \u002F MILP \u002F QP — see below) and **variable types**.\n\n## Choosing LP vs MILP vs QP\n\n**Decide from the objective and variables:**\n\n| If the objective is... | And variables are... | Use |\n|---|---|---|\n| Linear (sum of `c_i * x_i`) | All continuous | **LP** |\n| Linear | Some integer or binary | **MILP** |\n| Has squared (`x*x`) or cross (`x*y`) terms | Continuous (integer QP not supported) | **QP** (beta) |\n\n**Prefer LP when the problem allows it.** LP solves faster and has stronger optimality guarantees. Use MILP only when the problem logically requires whole numbers or yes\u002Fno decisions. Use QP only when the objective is genuinely quadratic (variance, squared error, kinetic energy).\n\n**Problem types that need extra care:** Multi-period planning and goal programming are easy to misinterpret. Double-check that rates and constraints apply to the right time period or priority level (AGENTS.md: verify understanding before code).\n\n- **Use LP** when every quantity can meaningfully be fractional: flows, proportions, rates, dollars, hours, tonnes of material, etc.\n- **Use MILP** when the problem mentions **counts** of discrete entities, **yes\u002Fno** choices, or **either\u002For** decisions (e.g. open a facility or not, assign a person to a shift, number of trucks).\n- **Use QP** when the objective minimizes variance, squared error, or any expression with `x*x` or `x*y` terms (portfolio optimization, least squares, regularized regression).\n\n## Integer vs continuous from wording\n\nChoose variable type from what the problem describes.\n\n| Problem wording \u002F concept | Variable type | Examples |\n|---------------------------|---------------|----------|\n| **Discrete entities (counts)** | **INTEGER** | Workers, cars, trucks, machines, pilots, facilities, units to manufacture (when \"units\" means whole items), trainees, vehicles |\n| **Yes\u002Fno or on\u002Foff** | **INTEGER** (binary, lb=0 ub=1) | Open a facility, run a machine, produce a product line, assign a person to a shift |\n| **Amounts that can be fractional** | **CONTINUOUS** | Tonnes, litres, dollars, hours, kWh, proportion of capacity, flow volume, weight |\n| **Rates or fractions** | **CONTINUOUS** | Utilization, percentage, share of budget |\n| **Unclear** | Prefer **INTEGER** if the noun is a countable thing (a worker, a car); prefer **CONTINUOUS** if it's a measure (amount of steel, hours worked). If the problem says \"whole\" or \"integer\" or \"number of\", use INTEGER. |\n\n**Rule of thumb:** If the quantity is \"how many *things*\" (people, vehicles, items, sites), use **INTEGER**. If it's \"how much\" (mass, volume, money, time) or a rate, use **CONTINUOUS** unless the problem explicitly requires whole numbers.\n\n## Quick Reference: Python API\n\n### LP Example\n\n```python\nfrom cuopt.linear_programming.problem import Problem, CONTINUOUS, MAXIMIZE\nfrom cuopt.linear_programming.solver_settings import SolverSettings\n\n# Create problem\nproblem = Problem(\"MyLP\")\n\n# Decision variables\nx = problem.addVariable(lb=0, vtype=CONTINUOUS, name=\"x\")\ny = problem.addVariable(lb=0, vtype=CONTINUOUS, name=\"y\")\n\n# Constraints\nproblem.addConstraint(2*x + 3*y \u003C= 120, name=\"resource_a\")\nproblem.addConstraint(4*x + 2*y \u003C= 100, name=\"resource_b\")\n\n# Objective\nproblem.setObjective(40*x + 30*y, sense=MAXIMIZE)\n\n# Solve\nsettings = SolverSettings()\nsettings.set_parameter(\"time_limit\", 60)\nproblem.solve(settings)\n\n# Check status (CRITICAL: use PascalCase!)\nif problem.Status.name in [\"Optimal\", \"PrimalFeasible\"]:\n    print(f\"Objective: {problem.ObjValue}\")\n    print(f\"x = {x.getValue()}\")\n    print(f\"y = {y.getValue()}\")\n```\n\n### MILP Example (with integer variables)\n\n```python\nfrom cuopt.linear_programming.problem import Problem, CONTINUOUS, INTEGER, MINIMIZE\n\nproblem = Problem(\"FacilityLocation\")\n\n# Binary variable (integer with bounds 0-1)\nopen_facility = problem.addVariable(lb=0, ub=1, vtype=INTEGER, name=\"open\")\n\n# Continuous variable\nproduction = problem.addVariable(lb=0, vtype=CONTINUOUS, name=\"production\")\n\n# Linking constraint: can only produce if facility is open\nproblem.addConstraint(production \u003C= 1000 * open_facility, name=\"link\")\n\n# Objective: fixed cost + variable cost\nproblem.setObjective(500*open_facility + 2*production, sense=MINIMIZE)\n\n# MILP-specific settings\nsettings = SolverSettings()\nsettings.set_parameter(\"time_limit\", 120)\nsettings.set_parameter(\"mip_relative_gap\", 0.01)  # 1% optimality gap\n\nproblem.solve(settings)\n\n# Check status\nif problem.Status.name in [\"Optimal\", \"FeasibleFound\"]:\n    print(f\"Open facility: {open_facility.getValue() > 0.5}\")\n    print(f\"Production: {production.getValue()}\")\n```\n\n### QP Example (beta — MINIMIZE only)\n\n```python\nfrom cuopt.linear_programming.problem import Problem, CONTINUOUS, MINIMIZE\nfrom cuopt.linear_programming.solver_settings import SolverSettings\n\n# Portfolio variance minimization\nproblem = Problem(\"Portfolio\")\nx1 = problem.addVariable(lb=0, ub=1, vtype=CONTINUOUS, name=\"stock_a\")\nx2 = problem.addVariable(lb=0, ub=1, vtype=CONTINUOUS, name=\"stock_b\")\nx3 = problem.addVariable(lb=0, ub=1, vtype=CONTINUOUS, name=\"stock_c\")\n\n# Quadratic objective (variance) — MUST be MINIMIZE\nproblem.setObjective(\n    0.04*x1*x1 + 0.02*x2*x2 + 0.01*x3*x3\n    + 0.02*x1*x2 + 0.01*x1*x3 + 0.016*x2*x3,\n    sense=MINIMIZE,\n)\n\n# Linear constraints\nproblem.addConstraint(x1 + x2 + x3 == 1, name=\"budget\")\nproblem.addConstraint(0.12*x1 + 0.08*x2 + 0.05*x3 >= 0.08, name=\"min_return\")\n\nproblem.solve(SolverSettings())\nif problem.Status.name in [\"Optimal\", \"PrimalFeasible\"]:\n    print(f\"Variance: {problem.ObjValue}\")\n```\n\n**QP rules:**\n- **MINIMIZE only** — solver rejects MAXIMIZE for quadratic objectives. To maximize `f(x)`, minimize `-f(x)`.\n- **Continuous variables only** — integer QP is not supported.\n- **Q should be PSD** (positive semi-definite) for a convex problem; otherwise the solver may return a non-optimal stationary point.\n- **Beta** — API may evolve; treat as production-capable for typical convex QP but expect occasional changes.\n\nSee `references\u002Fqp_examples.md` for least-squares, maximization-workaround, and matrix-form examples.\n\n## CRITICAL: Status Checking\n\n**Status values use PascalCase, NOT ALL_CAPS:**\n\n```python\n# ✅ CORRECT\nif problem.Status.name in [\"Optimal\", \"FeasibleFound\"]:\n    print(problem.ObjValue)\n\n# ❌ WRONG - will silently fail!\nif problem.Status.name == \"OPTIMAL\":  # Never matches!\n    print(problem.ObjValue)\n```\n\n**LP Status Values:** `Optimal`, `NoTermination`, `NumericalError`, `PrimalInfeasible`, `DualInfeasible`, `IterationLimit`, `TimeLimit`, `PrimalFeasible`\n\n**MILP Status Values:** `Optimal`, `FeasibleFound`, `Infeasible`, `Unbounded`, `TimeLimit`, `NoTermination`\n\n**QP Status Values:** Same set as LP. For QP debugging, print `f\"Actual status: '{problem.Status.name}'\"` and check that `Q` is PSD and variables are reasonably scaled.\n\n## Common Modeling Patterns\n\n### Binary Selection\n```python\n# Select exactly k items from n\nitems = [problem.addVariable(lb=0, ub=1, vtype=INTEGER) for _ in range(n)]\nproblem.addConstraint(sum(items) == k)\n```\n\n### Big-M Linking\n```python\n# If y=1, then x \u003C= 100; if y=0, x can be anything up to M\nM = 10000\nproblem.addConstraint(x \u003C= 100 + M*(1 - y))\n```\n\n### If-then \"must also produce\"\nWhen the problem says *if we do X then we must also do Y*, enforce both (i) the binary link and (ii) that Y is actually produced:\n```python\n# y_X \u003C= y_Y (if we do X, we must \"do\" Y)\nproblem.addConstraint(y_X \u003C= y_Y)\n# Production of Y when Y is chosen: produce at least 1 (or a minimum) when y_Y=1\nproblem.addConstraint(production_Y >= 1 * y_Y)  # or min_amount * y_Y\n```\nOtherwise the solver can set y_Y=1 but production_Y=0, satisfying the binary link but not the intent.\n\n### Building large expressions\nChained `+` over many terms can hit recursion limits in the API. Prefer building objectives and constraints with **LinearExpression**:\n```python\nfrom cuopt.linear_programming.problem import LinearExpression\n\n# Build as list of (vars, coeffs) instead of v1*c1 + v2*c2 + ...\nvars_list = [x, y, z]\ncoeffs_list = [\n    1.0,\n    2.0,\n    3.0,\n]\nexpr = LinearExpression(vars_list, coeffs_list, constant=0.0)\nproblem.addConstraint(expr \u003C= 100)\n```\nSee reference models in this skill's `assets\u002F` for examples.\n\n### Piecewise Linear (SOS2)\n```python\n# Approximate nonlinear function with breakpoints\n# Use lambda variables that sum to 1, at most 2 adjacent non-zero\n```\n\n## Solver Settings\n\n```python\nsettings = SolverSettings()\n\n# Time limit\nsettings.set_parameter(\"time_limit\", 60)\n\n# MILP gap tolerance (stop when within X% of optimal)\nsettings.set_parameter(\"mip_relative_gap\", 0.01)\n\n# Logging\nsettings.set_parameter(\"log_to_console\", 1)\n```\n\n## Common Issues\n\n| Problem | Likely Cause | Fix |\n|---------|--------------|-----|\n| Status never \"OPTIMAL\" | Using wrong case | Use `\"Optimal\"` not `\"OPTIMAL\"` |\n| Integer var has fractional value | Defined as CONTINUOUS | Use `vtype=INTEGER` |\n| Infeasible | Conflicting constraints | Check constraint logic |\n| Unbounded | Missing bounds | Add variable bounds |\n| Slow solve | Large problem | Set time limit, increase gap tolerance |\n| Maximum recursion depth | Building big expr with chained `+` | Use `LinearExpression(vars_list, coeffs_list, constant)` |\n| QP rejected with MAXIMIZE | QP only supports MINIMIZE | Negate the objective: minimize `-f(x)` |\n| QP returns non-optimal | Q not PSD or variables badly scaled | Check Q is PSD; rescale variables to similar magnitudes |\n\n## Getting Dual Values (LP only)\n\n```python\nif problem.Status.name == \"Optimal\":\n    constraint = problem.getConstraint(\"resource_a\")\n    shadow_price = constraint.DualValue\n    print(f\"Shadow price: {shadow_price}\")\n```\n\n## Reference Models\n\nAll reference models live in this skill's **`assets\u002F`** directory. Use them as reference when building new applications; do not edit them in place.\n\n### Minimal \u002F canonical examples (LP, MILP, QP)\n| Model | Type | Description |\n|-------|------|-------------|\n| [lp_basic](assets\u002Flp_basic\u002F) | LP | Minimal LP: variables, constraints, objective, solve |\n| [lp_duals](assets\u002Flp_duals\u002F) | LP | Dual values and reduced costs |\n| [lp_warmstart](assets\u002Flp_warmstart\u002F) | LP | PDLP warmstart for similar problems |\n| [milp_basic](assets\u002Fmilp_basic\u002F) | MILP | Minimal MIP; includes incumbent callback example |\n| [milp_production_planning](assets\u002Fmilp_production_planning\u002F) | MILP | Production planning with resource constraints |\n| [portfolio](assets\u002Fportfolio\u002F) | QP | Minimize portfolio variance; budget and min-return constraints |\n| [least_squares](assets\u002Fleast_squares\u002F) | QP | Minimize (x-3)² + (y-4)² (closest point) |\n| [maximization_workaround](assets\u002Fmaximization_workaround\u002F) | QP | Maximize quadratic via minimize -f(x) |\n\n### Other reference\n| Model | Type | Description |\n|-------|------|-------------|\n| [mps_solver](assets\u002Fmps_solver\u002F) | LP\u002FMILP | Solve any problem from standard MPS file format |\n\n**Quick command to list models:** `ls assets\u002F` (from this skill's directory).\n\n## When to Escalate\n\nUse troubleshooting and diagnostic guidance if:\n- Infeasible and you can't determine why\n- Numerical issues\n","# cuOpt Numerical Optimization Skill (Python)\n\nModel and solve LP, MILP, and QP problems using NVIDIA cuOpt's GPU-accelerated solver. The Python API surface (`Problem`, `SolverSettings`, `solve`) is shared across all three problem classes — only the objective form and a few rules change.\n\n## Before You Start\n\nUse a formulation summary (parameters, constraints, decisions, objective) if available; otherwise ask for decision variables, objective, and constraints. Then confirm **problem type** (LP \u002F MILP \u002F QP — see below) and **variable types**.\n\n## Choosing LP vs MILP vs QP\n\n**Decide from the objective and variables:**\n\n| If the objective is... | And variables are... | Use |\n|---|---|---|\n| Linear (sum of `c_i * x_i`) | All continuous | **LP** |\n| Linear | Some integer or binary | **MILP** |\n| Has squared (`x*x`) or cross (`x*y`) terms | Continuous (integer QP not supported) | **QP** (beta) |\n\n**Prefer LP when the problem allows it.** LP solves faster and has stronger optimality guarantees. Use MILP only when the problem logically requires whole numbers or yes\u002Fno decisions. Use QP only when the objective is genuinely quadratic (variance, squared error, kinetic energy).\n\n**Problem types that need extra care:** Multi-period planning and goal programming are easy to misinterpret. Double-check that rates and constraints apply to the right time period or priority level (AGENTS.md: verify understanding before code).\n\n- **Use LP** when every quantity can meaningfully be fractional: flows, proportions, rates, dollars, hours, tonnes of material, etc.\n- **Use MILP** when the problem mentions **counts** of discrete entities, **yes\u002Fno** choices, or **either\u002For** decisions (e.g. open a facility or not, assign a person to a shift, number of trucks).\n- **Use QP** when the objective minimizes variance, squared error, or any expression with `x*x` or `x*y` terms (portfolio optimization, least squares, regularized regression).\n\n## Integer vs continuous from wording\n\nChoose variable type from what the problem describes.\n\n| Problem wording \u002F concept | Variable type | Examples |\n|---------------------------|---------------|----------|\n| **Discrete entities (counts)** | **INTEGER** | Workers, cars, trucks, machines, pilots, facilities, units to manufacture (when \"units\" means whole items), trainees, vehicles |\n| **Yes\u002Fno or on\u002Foff** | **INTEGER** (binary, lb=0 ub=1) | Open a facility, run a machine, produce a product line, assign a person to a shift |\n| **Amounts that can be fractional** | **CONTINUOUS** | Tonnes, litres, dollars, hours, kWh, proportion of capacity, flow volume, weight |\n| **Rates or fractions** | **CONTINUOUS** | Utilization, percentage, share of budget |\n| **Unclear** | Prefer **INTEGER** if the noun is a countable thing (a worker, a car); prefer **CONTINUOUS** if it's a measure (amount of steel, hours worked). If the problem says \"whole\" or \"integer\" or \"number of\", use INTEGER. |\n\n**Rule of thumb:** If the quantity is \"how many *things*\" (people, vehicles, items, sites), use **INTEGER**. If it's \"how much\" (mass, volume, money, time) or a rate, use **CONTINUOUS** unless the problem explicitly requires whole numbers.\n\n## Quick Reference: Python API\n\n### LP Example\n\n```python\nfrom cuopt.linear_programming.problem import Problem, CONTINUOUS, MAXIMIZE\nfrom cuopt.linear_programming.solver_settings import SolverSettings\n\n# Create problem\nproblem = Problem(\"MyLP\")\n\n# Decision variables\nx = problem.addVariable(lb=0, vtype=CONTINUOUS, name=\"x\")\ny = problem.addVariable(lb=0, vtype=CONTINUOUS, name=\"y\")\n\n# Constraints\nproblem.addConstraint(2*x + 3*y \u003C= 120, name=\"resource_a\")\nproblem.addConstraint(4*x + 2*y \u003C= 100, name=\"resource_b\")\n\n# Objective\nproblem.setObjective(40*x + 30*y, sense=MAXIMIZE)\n\n# Solve\nsettings = SolverSettings()\nsettings.set_parameter(\"time_limit\", 60)\nproblem.solve(settings)\n\n# Check status (CRITICAL: use PascalCase!)\nif problem.Status.name in [\"Optimal\", \"PrimalFeasible\"]:\n    print(f\"Objective: {problem.ObjValue}\")\n    print(f\"x = {x.getValue()}\")\n    print(f\"y = {y.getValue()}\")\n```\n\n### MILP Example (with integer variables)\n\n```python\nfrom cuopt.linear_programming.problem import Problem, CONTINUOUS, INTEGER, MINIMIZE\n\nproblem = Problem(\"FacilityLocation\")\n\n# Binary variable (integer with bounds 0-1)\nopen_facility = problem.addVariable(lb=0, ub=1, vtype=INTEGER, name=\"open\")\n\n# Continuous variable\nproduction = problem.addVariable(lb=0, vtype=CONTINUOUS, name=\"production\")\n\n# Linking constraint: can only produce if facility is open\nproblem.addConstraint(production \u003C= 1000 * open_facility, name=\"link\")\n\n# Objective: fixed cost + variable cost\nproblem.setObjective(500*open_facility + 2*production, sense=MINIMIZE)\n\n# MILP-specific settings\nsettings = SolverSettings()\nsettings.set_parameter(\"time_limit\", 120)\nsettings.set_parameter(\"mip_relative_gap\", 0.01)  # 1% optimality gap\n\nproblem.solve(settings)\n\n# Check status\nif problem.Status.name in [\"Optimal\", \"FeasibleFound\"]:\n    print(f\"Open facility: {open_facility.getValue() > 0.5}\")\n    print(f\"Production: {production.getValue()}\")\n```\n\n### QP Example (beta — MINIMIZE only)\n\n```python\nfrom cuopt.linear_programming.problem import Problem, CONTINUOUS, MINIMIZE\nfrom cuopt.linear_programming.solver_settings import SolverSettings\n\n# Portfolio variance minimization\nproblem = Problem(\"Portfolio\")\nx1 = problem.addVariable(lb=0, ub=1, vtype=CONTINUOUS, name=\"stock_a\")\nx2 = problem.addVariable(lb=0, ub=1, vtype=CONTINUOUS, name=\"stock_b\")\nx3 = problem.addVariable(lb=0, ub=1, vtype=CONTINUOUS, name=\"stock_c\")\n\n# Quadratic objective (variance) — MUST be MINIMIZE\nproblem.setObjective(\n    0.04*x1*x1 + 0.02*x2*x2 + 0.01*x3*x3\n    + 0.02*x1*x2 + 0.01*x1*x3 + 0.016*x2*x3,\n    sense=MINIMIZE,\n)\n\n# Linear constraints\nproblem.addConstraint(x1 + x2 + x3 == 1, name=\"budget\")\nproblem.addConstraint(0.12*x1 + 0.08*x2 + 0.05*x3 >= 0.08, name=\"min_return\")\n\nproblem.solve(SolverSettings())\nif problem.Status.name in [\"Optimal\", \"PrimalFeasible\"]:\n    print(f\"Variance: {problem.ObjValue}\")\n```\n\n**QP rules:**\n- **MINIMIZE only** — solver rejects MAXIMIZE for quadratic objectives. To maximize `f(x)`, minimize `-f(x)`.\n- **Continuous variables only** — integer QP is not supported.\n- **Q should be PSD** (positive semi-definite) for a convex problem; otherwise the solver may return a non-optimal stationary point.\n- **Beta** — API may evolve; treat as production-capable for typical convex QP but expect occasional changes.\n\nSee `references\u002Fqp_examples.md` for least-squares, maximization-workaround, and matrix-form examples.\n\n## CRITICAL: Status Checking\n\n**Status values use PascalCase, NOT ALL_CAPS:**\n\n```python\n# ✅ CORRECT\nif problem.Status.name in [\"Optimal\", \"FeasibleFound\"]:\n    print(problem.ObjValue)\n\n# ❌ WRONG - will silently fail!\nif problem.Status.name == \"OPTIMAL\":  # Never matches!\n    print(problem.ObjValue)\n```\n\n**LP Status Values:** `Optimal`, `NoTermination`, `NumericalError`, `PrimalInfeasible`, `DualInfeasible`, `IterationLimit`, `TimeLimit`, `PrimalFeasible`\n\n**MILP Status Values:** `Optimal`, `FeasibleFound`, `Infeasible`, `Unbounded`, `TimeLimit`, `NoTermination`\n\n**QP Status Values:** Same set as LP. For QP debugging, print `f\"Actual status: '{problem.Status.name}'\"` and check that `Q` is PSD and variables are reasonably scaled.\n\n## Common Modeling Patterns\n\n### Binary Selection\n```python\n# Select exactly k items from n\nitems = [problem.addVariable(lb=0, ub=1, vtype=INTEGER) for _ in range(n)]\nproblem.addConstraint(sum(items) == k)\n```\n\n### Big-M Linking\n```python\n# If y=1, then x \u003C= 100; if y=0, x can be anything up to M\nM = 10000\nproblem.addConstraint(x \u003C= 100 + M*(1 - y))\n```\n\n### If-then \"must also produce\"\nWhen the problem says *if we do X then we must also do Y*, enforce both (i) the binary link and (ii) that Y is actually produced:\n```python\n# y_X \u003C= y_Y (if we do X, we must \"do\" Y)\nproblem.addConstraint(y_X \u003C= y_Y)\n# Production of Y when Y is chosen: produce at least 1 (or a minimum) when y_Y=1\nproblem.addConstraint(production_Y >= 1 * y_Y)  # or min_amount * y_Y\n```\nOtherwise the solver can set y_Y=1 but production_Y=0, satisfying the binary link but not the intent.\n\n### Building large expressions\nChained `+` over many terms can hit recursion limits in the API. Prefer building objectives and constraints with **LinearExpression**:\n```python\nfrom cuopt.linear_programming.problem import LinearExpression\n\n# Build as list of (vars, coeffs) instead of v1*c1 + v2*c2 + ...\nvars_list = [x, y, z]\ncoeffs_list = [\n    1.0,\n    2.0,\n    3.0,\n]\nexpr = LinearExpression(vars_list, coeffs_list, constant=0.0)\nproblem.addConstraint(expr \u003C= 100)\n```\nSee reference models in this skill's `assets\u002F` for examples.\n\n### Piecewise Linear (SOS2)\n```python\n# Approximate nonlinear function with breakpoints\n# Use lambda variables that sum to 1, at most 2 adjacent non-zero\n```\n\n## Solver Settings\n\n```python\nsettings = SolverSettings()\n\n# Time limit\nsettings.set_parameter(\"time_limit\", 60)\n\n# MILP gap tolerance (stop when within X% of optimal)\nsettings.set_parameter(\"mip_relative_gap\", 0.01)\n\n# Logging\nsettings.set_parameter(\"log_to_console\", 1)\n```\n\n## Common Issues\n\n| Problem | Likely Cause | Fix |\n|---------|--------------|-----|\n| Status never \"OPTIMAL\" | Using wrong case | Use `\"Optimal\"` not `\"OPTIMAL\"` |\n| Integer var has fractional value | Defined as CONTINUOUS | Use `vtype=INTEGER` |\n| Infeasible | Conflicting constraints | Check constraint logic |\n| Unbounded | Missing bounds | Add variable bounds |\n| Slow solve | Large problem | Set time limit, increase gap tolerance |\n| Maximum recursion depth | Building big expr with chained `+` | Use `LinearExpression(vars_list, coeffs_list, constant)` |\n| QP rejected with MAXIMIZE | QP only supports MINIMIZE | Negate the objective: minimize `-f(x)` |\n| QP returns non-optimal | Q not PSD or variables badly scaled | Check Q is PSD; rescale variables to similar magnitudes |\n\n## Getting Dual Values (LP only)\n\n```python\nif problem.Status.name == \"Optimal\":\n    constraint = problem.getConstraint(\"resource_a\")\n    shadow_price = constraint.DualValue\n    print(f\"Shadow price: {shadow_price}\")\n```\n\n## Reference Models\n\nAll reference models live in this skill's **`assets\u002F`** directory. Use them as reference when building new applications; do not edit them in place.\n\n### Minimal \u002F canonical examples (LP, MILP, QP)\n| Model | Type | Description |\n|-------|------|-------------|\n| [lp_basic](assets\u002Flp_basic\u002F) | LP | Minimal LP: variables, constraints, objective, solve |\n| [lp_duals](assets\u002Flp_duals\u002F) | LP | Dual values and reduced costs |\n| [lp_warmstart](assets\u002Flp_warmstart\u002F) | LP | PDLP warmstart for similar problems |\n| [milp_basic](assets\u002Fmilp_basic\u002F) | MILP | Minimal MIP; includes incumbent callback example |\n| [milp_production_planning](assets\u002Fmilp_production_planning\u002F) | MILP | Production planning with resource constraints |\n| [portfolio](assets\u002Fportfolio\u002F) | QP | Minimize portfolio variance; budget and min-return constraints |\n| [least_squares](assets\u002Fleast_squares\u002F) | QP | Minimize (x-3)² + (y-4)² (closest point) |\n| 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Triggers include \"check my Slack\", \"what channels have unreads\", \"send a message to\", \"search Slack for\", \"extract from Slack\", \"find who said\", or any task requiring programmatic Slack interaction.","https:\u002F\u002Fgithub.com\u002FYYC-Cube\u002FYYC3-Knowledge-Base\u002Fblob\u002Fmain\u002FYYC3-WebSpec-Web标准\u002FYYC3-WebSpec-Web标准-standards\u002Fbrowser-agent\u002Fskills\u002Fslack\u002FSKILL.md",[],[],{"skillNo":201,"name":202,"nameZh":6,"description":203,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":189,"licenseFileUrl":6,"sourceHtmlUrl":204,"categories":205,"keywords":206,"publishedAt":19},"01M7CTCSSB8ZP3Q58C3YZDZK1W","electron","Automate Electron desktop apps (VS Code, Slack, Discord, Figma, Notion, Spotify, etc.) using agent-browser via Chrome DevTools Protocol. Use when the user needs to interact with an Electron app, automate a desktop app, connect to a running app, control a native app, or test an Electron application. Triggers include \"automate Slack app\", \"control VS Code\", \"interact with Discord app\", \"test this Electron app\", \"connect to desktop app\", or any task requiring automation of a native Electron application.","https:\u002F\u002Fgithub.com\u002FYYC-Cube\u002FYYC3-Knowledge-Base\u002Fblob\u002Fmain\u002FYYC3-WebSpec-Web标准\u002FYYC3-WebSpec-Web标准-standards\u002Fbrowser-agent\u002Fskills\u002Felectron\u002FSKILL.md",[],[],{"skillNo":208,"name":209,"nameZh":6,"description":210,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":189,"licenseFileUrl":6,"sourceHtmlUrl":211,"categories":212,"keywords":213,"publishedAt":19},"01M7CTCBJY76688V4DCZGWFHGQ","dogfood","Systematically explore and test a web application to find bugs, UX issues, and other problems. Use when asked to \"dogfood\", \"QA\", \"exploratory test\", \"find issues\", \"bug hunt\", \"test this app\u002Fsite\u002Fplatform\", or review the quality of a web application. Produces a structured report with full reproduction evidence -- step-by-step screenshots, repro videos, and detailed repro steps for every issue -- so findings can be handed directly to the responsible teams.","https:\u002F\u002Fgithub.com\u002FYYC-Cube\u002FYYC3-Knowledge-Base\u002Fblob\u002Fmain\u002FYYC3-WebSpec-Web标准\u002FYYC3-WebSpec-Web标准-standards\u002Fbrowser-agent\u002Fskills\u002Fdogfood\u002FSKILL.md",[],[],{"skillNo":215,"name":216,"nameZh":6,"description":217,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":189,"licenseFileUrl":6,"sourceHtmlUrl":218,"categories":219,"keywords":220,"publishedAt":19},"01M7CTC4H0FFGVEAQR9PA4GA1A","agent-browser","Browser automation CLI for AI agents. Use when the user needs to interact with websites, including navigating pages, filling forms, clicking buttons, taking screenshots, extracting data, testing web apps, or automating any browser task. Triggers include requests to \"open a website\", \"fill out a form\", \"click a button\", \"take a screenshot\", \"scrape data from a page\", \"test this web app\", \"login to a site\", \"automate browser actions\", or any task requiring programmatic web interaction.","https:\u002F\u002Fgithub.com\u002FYYC-Cube\u002FYYC3-Knowledge-Base\u002Fblob\u002Fmain\u002FYYC3-WebSpec-Web标准\u002FYYC3-WebSpec-Web标准-standards\u002Fbrowser-agent\u002Fskills\u002Fagent-browser\u002FSKILL.md",[],[],{"skillNo":222,"name":223,"nameZh":6,"description":224,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":189,"licenseFileUrl":6,"sourceHtmlUrl":225,"categories":226,"keywords":227,"publishedAt":19},"01M7CTBKVFYBG78FDSABSDJTTQ","shadcn","Manages shadcn components and projects — adding, searching, fixing, debugging, styling, and composing UI, including chat interfaces. Provides project context, component docs, and usage examples. Applies when working with shadcn\u002Fui, component registries, presets, --preset codes, or any project with a components.json file. Also triggers for \"shadcn init\", \"create an app with --preset\", \"switch to --preset\", and for building a design system or applying a DESIGN.md or brand spec to shadcn\u002Fui.","https:\u002F\u002Fgithub.com\u002FYYC-Cube\u002FYYC3-Knowledge-Base\u002Fblob\u002Fmain\u002FYYC3-UI-界面组件\u002FYYC3-UI-界面组件-ui\u002Fskills\u002Fshadcn\u002FSKILL.md",[],[]]