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2. LP-type problem - Wikipedia

   en.wikipedia.org/wiki/LP-type_problem

   The discovery of linear time algorithms for linear programming and the observation that the same algorithms could in many cases be used to solve geometric optimization problems that were not linear programs goes back at least to Megiddo (1983, 1984), who gave a linear expected time algorithm for both three-variable linear programs and the ...

3. Basic solution (linear programming) - Wikipedia

   en.wikipedia.org/wiki/Basic_solution_(Linear...

   In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions. For a polyhedron P {\displaystyle P} and a vector x ∗ ∈ R n {\displaystyle \mathbf {x} ^{*}\in \mathbb {R} ^{n}} , x ∗ {\displaystyle \mathbf {x} ^{*}} is a ...

4. Linear complementarity problem - Wikipedia

   en.wikipedia.org/wiki/Linear_complementarity_problem

   The minimum of f is 0 at z if and only if z solves the linear complementarity problem. If M is positive definite, any algorithm for solving (strictly) convex QPs can solve the LCP. Specially designed basis-exchange pivoting algorithms, such as Lemke's algorithm and a variant of the simplex algorithm of Dantzig have been used for decades ...

5. 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 ...

6. Linear programming - Wikipedia

   en.wikipedia.org/wiki/Linear_programming

   However, some problems have distinct optimal solutions; for example, the problem of finding a feasible solution to a system of linear inequalities is a linear programming problem in which the objective function is the zero function (i.e., the constant function taking the value zero everywhere).

7. 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 ]