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2. lp_solve - Wikipedia

   en.wikipedia.org/wiki/Lp_solve

   lp_solve is a free software command line utility and library for solving linear programming and mixed integer programming problems. It ships with support for two file formats, MPS and lp_solve's own LP format. [ 1 ]

3. LP-type problem - Wikipedia

   en.wikipedia.org/wiki/LP-type_problem

   By using the recursive algorithm to solve a given problem, switching to the iterative algorithm for its recursive calls, and then switching again to Seidel's algorithm for the calls made by the iterative algorithm, it is possible solve a given LP-type problem using O(dn + d! d O(1) log n) violation tests.

4. HiGHS optimization solver - Wikipedia

   en.wikipedia.org/wiki/HiGHS_optimization_solver

   HiGHS has an interior point method implementation for solving LP problems, based on techniques described by Schork and Gondzio (2020). [10] It is notable for solving the Newton system iteratively by a preconditioned conjugate gradient method, rather than directly, via an LDL* decomposition. The interior point solver's performance relative to ...

5. Farkas' lemma - Wikipedia

   en.wikipedia.org/wiki/Farkas'_lemma

   Farkas's lemma can be varied to many further theorems of alternative by simple modifications, [5] such as Gordan's theorem: Either < has a solution x, or = has a nonzero solution y with y ≥ 0. Common applications of Farkas' lemma include proving the strong duality theorem associated with linear programming and the Karush–Kuhn–Tucker ...

6. Linear programming - Wikipedia

   en.wikipedia.org/wiki/Linear_programming

   Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization).

7. Branch and cut - Wikipedia

   en.wikipedia.org/wiki/Branch_and_cut

   This description assumes the ILP is a maximization problem.. The method solves the linear program without the integer constraint using the regular simplex algorithm.When an optimal solution is obtained, and this solution has a non-integer value for a variable that is supposed to be integer, a cutting plane algorithm may be used to find further linear constraints which are satisfied by all ...

8. Karmarkar's algorithm - Wikipedia

   en.wikipedia.org/wiki/Karmarkar's_algorithm

   Karmarkar's algorithm is an algorithm introduced by Narendra Karmarkar in 1984 for solving linear programming problems. It was the first reasonably efficient algorithm that solves these problems in polynomial time. The ellipsoid method is also polynomial time but proved to be inefficient in practice.

9. Linear programming relaxation - Wikipedia

   en.wikipedia.org/wiki/Linear_programming_relaxation

   Two 0–1 integer programs that are equivalent, in that they have the same objective function and the same set of feasible solutions, may have quite different linear programming relaxations: a linear programming relaxation can be viewed geometrically, as a convex polytope that includes all feasible solutions and excludes all other 0–1 vectors ...