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LibraryOptimization

Linear Programming

Linear programming (LP) is a mathematical optimization technique for maximizing or minimizing a linear objective function subject to linear equality and inequality constraints. It provides a systematic way to allocate limited resources—such as time, money, or materials—across competing activities. LP is foundational in operations research, powering decision-making in logistics, finance, manufacturing, and many AI/ML pipelines for constrained optimization.

by N/A – mathematical method, not a productAcademic

Key Features

  • •Linear objective and constraints: models problems with a linear objective function and linear equality/inequality constraints.
  • •Convexity and global optimality: feasible region is a convex polytope, guaranteeing any local optimum is a global optimum.
  • •Standardized formulations: canonical forms (standard, slack, dual) enable systematic modeling and analysis.
  • •Efficient solvers: mature algorithms like simplex, interior-point, and barrier methods with highly optimized commercial and open-source solvers.
  • •Duality theory: every LP has a dual problem, providing sensitivity analysis and economic interpretation of shadow prices.

Pricing

OpenSource

Linear programming as a mathematical technique is free to use; pricing applies only to specific solver implementations (e.g., commercial solvers like Gurobi or CPLEX use paid/enterprise licensing, while solvers like GLPK and CBC are open source).

Alternatives

Mixed-Integer Linear Programming (MILP)Quadratic Programming (QP)Nonlinear Programming (NLP)Constraint Programming (CP)Heuristics and Metaheuristics (e.g., Genetic Algorithms, Simulated Annealing)

Links

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Industries Using Linear Programming

manufacturing11energy4retail4transportation4pharmaceuticalsBiotech1advertising1aerospace defense1architecture and interior design1

Often Used With

Time-Series Forecasting (11)Routing & Scheduling (8)LLM (5)Combinatorial Optimization (2)Google OR-Tools (2)Classical ML (2)Quantum Annealer (1)Reinforcement Learning (unspecified framework) (1)Reinforcement Learning (1)Mixed-Integer Programming (1)Anomaly Detection (1)Workflow Orchestration (1)

Quick Stats

30
Total Use Cases
11
Industries
12
Related Technologies