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2. Integer programming - Wikipedia

   en.wikipedia.org/wiki/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 .

3. List of optimization software - Wikipedia

   en.wikipedia.org/wiki/List_of_optimization_software

   solver for mixed integer programming (MIP) and mixed integer nonlinear programming (MINLP). SciPy: BSD general numeric package for Python, with some support for optimization. Uno: MIT Lagrange-Newton solver that unifies nonconvex optimization, implemented in C++. Developed at Argonne National Laboratory and Zuse Institute Berlin. [3]

4. HiGHS optimization solver - Wikipedia

   en.wikipedia.org/wiki/HiGHS_optimization_solver

   HiGHS is open-source software to solve linear programming (LP), mixed-integer programming (MIP), and convex quadratic programming (QP) models. [1] Written in C++ and published under an MIT license, HiGHS provides programming interfaces to C, Python, Julia, Rust, R, JavaScript, Fortran, and C#. It has no external dependencies.

5. Lenstra–Lenstra–Lovász lattice basis reduction algorithm

   en.wikipedia.org/wiki/Lenstra–Lenstra–Lovász...

   The original applications were to give polynomial-time algorithms for factorizing polynomials with rational coefficients, for finding simultaneous rational approximations to real numbers, and for solving the integer linear programming problem in fixed dimensions.

6. CPLEX - Wikipedia

   en.wikipedia.org/wiki/CPLEX

   The IBM ILOG CPLEX Optimizer solves integer programming problems, very large [3] linear programming problems using either primal or dual variants of the simplex method or the barrier interior point method, convex and non-convex quadratic programming problems, and convex quadratically constrained problems (solved via second-order cone programming, or SOCP).

7. Branch and cut - Wikipedia

   en.wikipedia.org/wiki/Branch_and_cut

   Branch and cut [1] is a method of combinatorial optimization for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some or all the unknowns are restricted to integer values. [2] Branch and cut involves running a branch and bound algorithm and using cutting planes to tighten

8. List of numerical analysis topics - Wikipedia

   en.wikipedia.org/wiki/List_of_numerical_analysis...

   Linear programming (also treats integer programming) — objective function and constraints are linear Algorithms for linear programming: Simplex algorithm. Bland's rule — rule to avoid cycling in the simplex method; Klee–Minty cube — perturbed (hyper)cube; simplex method has exponential complexity on such a domain

9. Cutting stock problem - Wikipedia

   en.wikipedia.org/wiki/Cutting_stock_problem

   It is an optimization problem in mathematics that arises from applications in industry. In terms of computational complexity, the problem is an NP-hard problem reducible to the knapsack problem. The problem can be formulated as an integer linear programming problem.