integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers...

be integers, then the problem is called an integer programming (IP) or integer linear programming (ILP) problem. In contrast to linear programming, which...

linear constraints on the variables. Quadratic programming is a type of nonlinear programming. "Programming" in this context refers to a formal procedure...

programming relaxation has a value differing from that of the unrelaxed 0–1 integer program. The linear programming relaxation of an integer program may...

GNU Linear Programming Kit (GLPK) is a software package intended for solving large-scale linear programming (LP), mixed integer programming (MIP), and...

for writing integer literals in many programming languages: Many programming languages, especially those influenced by C, prefix an integer literal with...

cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not...

among them: Linear programming Quadratic programming Nonlinear programming Mixed-integer programming Mixed-integer quadratic programming with or without...

may be analyzed using graph-theoretic methods, by dynamic programming, or by integer programming. Let G = ( V , E ) {\displaystyle G=(V,E)} be an undirected...

optimizer) a software package for linear programming, integer programming, nonlinear programming, stochastic programming, and global optimization. The "What's...

formulated as a quadratically constrained quadratic program. Since 0–1 integer programming is NP-hard in general, QCQP is also NP-hard. However, even for a...

that deals with problems that are not linear. Let n, m, and p be positive integers. Let X be a subset of Rn (usually a box-constrained one), let f, gi, and...

problems on graphs, matroids and other discrete structures integer programming constraint programming These branches are all closely intertwined however, since...

closely connected to the theory of linear programming and integer programming. Both linear programs and integer programs are expressed in canonical form as seeking...

by IBM. The IBM ILOG CPLEX Optimizer solves integer programming problems, very large linear programming problems using either primal or dual variants...

solutions, integer programming etc. Some versions of the map label placement problem can be formulated as multiple choices integer programming (MCIP) problems...

In computer programming, an integer overflow occurs when an arithmetic operation on integers attempts to create a numeric value that is outside of the...

prove that an integer programming problem whose constraint matrix is totally unimodular and whose right-hand side is integer, has integer basic solutions...

This approach is used for a number of NP-hard problems: Integer programming Nonlinear programming Travelling salesman problem (TSP) Quadratic assignment...

transformed into a convex program. Integer programming studies linear programs in which some or all variables are constrained to take on integer values. This is...

non-negative. In pure integer programming problems, the feasible set is the set of integers (or some subset thereof). In linear programming problems, the feasible...

check convex hull (integer) affine hull integer projection computing the lexicographic minimum using parametric integer programming coalescing parametric...

Dynamic programming is both a mathematical optimization method and an algorithmic paradigm. The method was developed by Richard Bellman in the 1950s and...

bases enable iterative solutions of linear and various nonlinear integer programming problems in polynomial time. They were introduced by Jack E. Graver...

6(8):11472 (2011). Glover, Fred (January 1986). "Future paths for integer programming and links to artificial intelligence" (PDF). Computers and Operations...

the programmer intends to use the data. Most programming languages support basic data types of integer numbers (of varying sizes), floating-point numbers...

Semidefinite programming (SDP) is a subfield of mathematical programming concerned with the optimization of a linear objective function (a user-specified...

PA is in P, and this extends to fixed-dimensional parametric integer linear programming. Because Presburger arithmetic is decidable, automatic theorem...

variables, rather than individual variables, as in ordinary mixed integer programming. Knowing that a variable is part of a set and that it is ordered...

integers Chance constrained programming for dealing with constraints that must be satisfied with a given probability Stochastic dynamic programming Markov...