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2. Linear programming - Wikipedia

   en.wikipedia.org/wiki/Linear_programming

   Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. Its feasible region is a convex polytope, which is a set defined as the ...

3. Simplex algorithm - Wikipedia

   en.wikipedia.org/wiki/Simplex_algorithm

   Simplex algorithm. In mathematical optimization, Dantzig 's simplex algorithm (or simplex method) is a popular algorithm for linear programming. [1] The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin. [2] Simplices are not actually used in the method, but one interpretation of it is that it ...

4. Integer programming - Wikipedia

   en.wikipedia.org/wiki/Integer_programming

   Integer programming. An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear.

5. Dantzig–Wolfe decomposition - Wikipedia

   en.wikipedia.org/wiki/Dantzig–Wolfe_decomposition

   Dantzig–Wolfe decomposition is an algorithm for solving linear programming problems with special structure. It was originally developed by George Dantzig and Philip Wolfe and initially published in 1960. [1] Many texts on linear programming have sections dedicated to discussing this decomposition algorithm. [2][3][4][5][6][7] Dantzig–Wolfe ...

6. Successive linear programming - Wikipedia

   en.wikipedia.org/wiki/Successive_linear_programming

   Successive linear programming. Successive Linear Programming (SLP), also known as Sequential Linear Programming, is an optimization technique for approximately solving nonlinear optimization problems. [1] It is related to, but distinct from, quasi-Newton methods. Starting at some estimate of the optimal solution, the method is based on solving ...

7. Linear programming relaxation - Wikipedia

   en.wikipedia.org/wiki/Linear_programming_relaxation

   In mathematics, the relaxation of a (mixed) integer linear program is the problem that arises by removing the integrality constraint of each variable. For example, in a 0–1 integer program, all constraints are of the form. . The relaxation of the original integer program instead uses a collection of linear constraints.

8. Linear-fractional programming - Wikipedia

   en.wikipedia.org/wiki/Linear-fractional_programming

   Formally, a linear-fractional program is defined as the problem of maximizing (or minimizing) a ratio of affine functions over a polyhedron, where represents the vector of variables to be determined, and are vectors of (known) coefficients, is a (known) matrix of coefficients and are constants. The constraints have to restrict the feasible ...

9. GLOP - Wikipedia

   en.wikipedia.org/wiki/GLOP

   GLOP. GLOP (the Google Linear Optimization Package) is Google 's open source linear programming solver, created by Google's Operations Research Team. It is written in C++ and was released to the public as part of Google's OR-Tools software suite in 2014. [ 1] GLOP uses a revised primal-dual simplex algorithm optimized for sparse matrices. It ...