Skill

role-algorithms:mathematical-optimization

Applies mathematical optimization — linear programming (simplex, interior point, duality), integer/mixed-integer programming (branch-and-bound, cutting planes), convex optimization (gradient descent variants, Adam, L-BFGS, Newton), constraint satisfaction (backtracking, AC-3, SAT/SMT solvers), and combinatorial optimization (VRP, scheduling, assignment, bin packing). Use when formulating optimization problems, selecting solvers, or solving scheduling/allocation/routing problems.

Install

npx claudepluginhub rnavarych/alpha-engineer --plugin role-algorithms

Tool Access

This skill is limited to using the following tools:

ReadGrepGlobBash

Preview

- Formulating a real-world problem as a mathematical optimization model

Supporting Assets

references/constraint-and-combinatorial.mdreferences/convex-and-gradient.mdreferences/linear-and-integer-programming.md

SKILL.md

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Parent Repo Stars9

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Last CommitMar 3, 2026

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role-algorithms:mathematical-optimization

When to use

Formulating a real-world problem as a mathematical optimization model

Choosing between LP, MIP, convex, CSP, or combinatorial approaches

Selecting the right gradient descent variant for a machine learning or fitting problem

Solving scheduling, assignment, routing, or bin packing problems

Applying SAT/SMT solvers or constraint programming for logical constraint problems

Evaluating solver options (PuLP, CVXPY, OR-Tools, Gurobi, Z3)

Core principles

Formulate before you code — identify variables, objective, and constraints explicitly before touching a solver

Tight LP relaxation = faster MIP — every improvement to the relaxation bound shrinks the branch-and-bound tree

Convexity is the dividing line — convex problems are reliably solvable; non-convex require restarts and heuristics

Adam is not always the answer — L-BFGS beats Adam on smooth well-conditioned problems with moderate dimension

CP-SAT over custom backtracking — Google OR-Tools CP-SAT handles constraint propagation and search orders better than hand-rolled solvers

Reference Files

references/linear-and-integer-programming.md — LP formulation, simplex vs interior point, duality and shadow prices, MIP branch-and-bound, Big-M method, symmetry breaking, solver library options

references/convex-and-gradient.md — convexity verification (Hessian PSD), gradient descent variants (SGD, Adam, L-BFGS), Newton/conjugate gradient second-order methods, CVXPY/SciPy/JAX tooling

references/constraint-and-combinatorial.md — CSP formulation, backtracking + constraint propagation, SAT/SMT solvers (Z3, CDCL), VRP/scheduling/assignment/bin packing patterns, problem classification guide

Mathematical Optimization

When to use

Formulating a real-world problem as a mathematical optimization model
Choosing between LP, MIP, convex, CSP, or combinatorial approaches
Selecting the right gradient descent variant for a machine learning or fitting problem
Solving scheduling, assignment, routing, or bin packing problems
Applying SAT/SMT solvers or constraint programming for logical constraint problems
Evaluating solver options (PuLP, CVXPY, OR-Tools, Gurobi, Z3)

Core principles

Formulate before you code — identify variables, objective, and constraints explicitly before touching a solver
Tight LP relaxation = faster MIP — every improvement to the relaxation bound shrinks the branch-and-bound tree
Convexity is the dividing line — convex problems are reliably solvable; non-convex require restarts and heuristics
Adam is not always the answer — L-BFGS beats Adam on smooth well-conditioned problems with moderate dimension
CP-SAT over custom backtracking — Google OR-Tools CP-SAT handles constraint propagation and search orders better than hand-rolled solvers

Reference Files

references/linear-and-integer-programming.md — LP formulation, simplex vs interior point, duality and shadow prices, MIP branch-and-bound, Big-M method, symmetry breaking, solver library options
references/convex-and-gradient.md — convexity verification (Hessian PSD), gradient descent variants (SGD, Adam, L-BFGS), Newton/conjugate gradient second-order methods, CVXPY/SciPy/JAX tooling
references/constraint-and-combinatorial.md — CSP formulation, backtracking + constraint propagation, SAT/SMT solvers (Z3, CDCL), VRP/scheduling/assignment/bin packing patterns, problem classification guide