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...

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

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

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

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...

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

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...

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

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...

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

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

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

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

An integer is the number zero (0), a positive natural number (1, 2, 3, . . .), or the negation of a positive natural number (−1, −2, −3, . . .). The negations...

Dynamic Programming in Macroeconomic Models." An introduction to dynamic programming as an important tool in economic theory. Dynamic Programming: from...

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

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

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

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

"Simplex algorithms". In J. E. Beasley (ed.). Advances in linear and integer programming. Oxford Science. pp. 1–46. MR 1438309. Maros, István (2003). Computational...

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

diverse range of SQP methods. Sequential linear programming Sequential linear-quadratic programming Augmented Lagrangian method SQP methods have been...

combinatorial optimization for solving integer linear programming (ILP) and mixed integer linear programming (MILP) problems with many variables. The...

satisfaction problem Cutting stock problem Dominating set problem Integer programming Job shop scheduling Knapsack problem Minimum relevant variables in...

multiparametric programming problem If integer variables are present, then the problem is referred to as (multi)parametric mixed-integer programming problem If...

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