Linked from

The 61 pages that link to Linear programming, each with the reason it gives.

• Graph theoryCompared with: Optimization problems on graphs can often be formulated and solved through linear programming.

• Convex setBroader topic: Its feasible regions are polyhedra, a central class of convex sets.

• Lagrange multiplierCompared with: Its optima often occur at boundary vertices, where smooth multiplier conditions alone may not suffice.

• Operations researchBroader topic: It models resource-allocation decisions with explicit objectives and limits.

• Gaussian eliminationRelated: Its algorithms repeatedly solve linear systems involving constraints and candidate solution directions.

• Economic planningRelated: It formalizes how planners can allocate limited resources among competing goals.

• Convex optimizationBroader topic: It is the foundational special case of convex optimization.

• Linear equationRelated: Its equality constraints are linear equations defining feasible solutions.

• Convex functionRelated: Its development helped make convexity practically central to twentieth-century optimization.

• Dynamic programmingCompared with: It offers a different formulation for some optimization problems with continuous variables.

• Integer programmingNarrower topic: Integer programming adds discrete restrictions to this continuous optimization framework.

• Constraint satisfaction problemCompared with: Its algebraic restrictions differ from the arbitrary discrete constraints common in CSPs.

• Nonlinear systemCompared with: Its linear structure enables guarantees and algorithms unavailable for general nonlinear optimization.

• PolyhedronRelated: Its feasible regions are polyhedra, and bounded optima occur at extreme points.

• Constrained optimizationBroader topic: It is the tractable, widely used case where both the objective and restrictions are linear.

• InequalityRelated: Its feasible region is defined by simultaneous inequalities.

• Assignment problemRelated: Binary assignment decisions have an integral linear-programming formulation.

• Convex geometryBroader topic: Its feasible regions are polyhedra, a central class of convex sets.

• Extreme pointRelated: When an optimum exists on a polytope, some extreme point attains it.

• Maximum flow problemNarrower topic: Maximum flow is a structured linear program with special graph algorithms and integral solutions.

• Feasible regionNarrower topic: Its constraints produce a particularly structured feasible region: a polyhedron.

• Linear programming dualityNarrower topic: Duality is a structural theorem about this class of optimization problems.

• ConvexityBroader topic: Its feasible region is a convex polyhedron, making it a foundational convex optimization problem.

• Optimal controlCompared with: It handles static decision variables, whereas optimal control chooses functions constrained by dynamics.

• Carathéodory's theoremRelated: Extreme-point solutions and basic feasible solutions reflect dimension-bounded convex representations.

• Flow conservationRelated: Flow conservation equations are linear constraints in network optimization.

• Karush–Kuhn–Tucker conditionsRelated: KKT conditions specialize to the optimality relations behind linear-programming duality.

• Convex polygonRelated: In two variables, feasible regions are intersections of half-planes and may be convex polygons.

• Linear functionalRelated: Its objective is a linear functional evaluated on feasible vectors.

• Mathematical optimizationBroader topic: It models resource allocation when effects and limits are linear.

• Minimax theoremRelated: A finite zero-sum game can be solved through a pair of dual linear programs.

• Simplex algorithmNarrower topic: It is the problem class the simplex algorithm is designed to solve.

• Transportation problemNarrower topic: The transportation problem is a structured linear program with shipment quantities as decision variables.

• Convex analysisBroader topic: It is a foundational convex problem with geometric and dual interpretations.

• Ford–Fulkerson algorithmRelated: A flow network’s maximum-flow problem can also be expressed as a linear program.

• Interior-point methodRelated: Interior-point methods became a major alternative to the simplex method for linear programs.

• Optimization problemBroader topic: It is a tractable, widely used subclass with a distinctive geometric solution structure.

• Polynomial timeBroader topic: Interior-point methods solve linear programs in polynomial time.

• Convex bodyRelated: Polyhedral convex bodies encode feasible regions and their extreme-point solutions.

• Linear programming relaxationBroader topic: The relaxation is solved as an ordinary linear program.

• Tjalling KoopmansNarrower topic: Activity analysis formulates resource allocation as a linear optimization problem.

• George DantzigRelated: Dantzig’s algorithm made this framework broadly usable, though this page links to it under mechanism.

• Maximum and minimumBroader topic: Its finite optima, when they exist, occur at vertices of the feasible region.

• Nonlinear programmingCompared with: Its polyhedral geometry and mature algorithms differ sharply from general nonlinear models.

• Circulation problemNarrower topic: Circulation feasibility is a linear system with bounds, and its cost variants are linear programs.

• Helly's theoremRelated: Helly-type arguments yield bounds on infeasible constraint subsystems.

• Numerical optimizationBroader topic: It is a structured special case with efficient algorithms and strong global guarantees.

• Farkas' lemmaRelated: The lemma became a central tool for proving results about linear optimization.

• Leonid KantorovichBroader topic: Kantorovich developed the method to solve production and resource-allocation problems.

• Minimum-cost flow problemNarrower topic: The problem is a structured linear program with network-specific variables and constraints.