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
The resulting relaxation is a linear program, hence the name. This relaxation technique transforms an NP-hard optimization problem (integer programming) into a related problem that is solvable in polynomial time (linear programming); the solution to the relaxed linear program can be used to gain information about the solution to the original integer program.
and 23 Related for: Linear programming relaxation information
the solution to the original integer program. Consider the set cover problem, the linearprogrammingrelaxation of which was first considered by Lovász...
and objective are represented by linear relationships. Linearprogramming is a special case of mathematical programming (also known as mathematical optimization)...
integer linearprogramming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is...
the linearprogrammingrelaxation of traditional graph coloring. Indeed, fractional coloring problems are much more amenable to a linearprogramming approach...
(optimization) Semidefinite programmingRelaxation (approximation) Gärtner, Bernd; Matoušek, Jiří (2006). Understanding and Using LinearProgramming. Berlin: Springer...
cutting planes to tighten the linearprogrammingrelaxations. Note that if cuts are only used to tighten the initial LP relaxation, the algorithm is called...
appropriate rounding. The popular relaxations include the following. Linearprogrammingrelaxations Semidefinite programmingrelaxations Primal-dual methods Dual...
added to the linearprogrammingrelaxation (LP relaxation). At the start of the algorithm, sets of columns are excluded from the LP relaxation in order to...
large instances of protein design problems. These solvers use a linearprogrammingrelaxation of the problem, where qi and qij are allowed to take continuous...
pseudo-disks-set with n objects and union complexity u. Using linearprogrammingrelaxation, it is possible to find a disjoint set of size at least n u...
solved as an integer linearprogram (ILP). Compute an optimal fractional solution x {\displaystyle x} to the linearprogrammingrelaxation (LP) of the ILP...
Semidefinite programming (SDP) is a subfield of mathematical programming concerned with the optimization of a linear objective function (a user-specified...
and superdiagonals. Linear independence — two or more vectors are linearly independent if there is no way to construct one from linear combinations of the...
algorithm for the minimum vertex cover problem. Furthermore, the linearprogrammingrelaxation of that ILP is half-integral, that is, there exists an optimal...
4 Linearprogramming problems are the simplest convex programs. In LP, the objective and constraint functions are all linear. Quadratic programming are...
approximation for the weighted case. Using the technique of Linearprogrammingrelaxation, it is possible to approximate the optimal scheduling with slightly...
over-relaxation Iterative method § Linear systems Gaussian Belief Propagation Matrix splitting Saad, Yousef (2003). Iterative Methods for Sparse Linear Systems...
second-order cone programming (SOCP) and linearprogramming (LP) relaxations providing the same objective value as the SDP relaxation are available. Nonconvex...
{\displaystyle \ln(4)+\varepsilon \leq 1.39} approximation using a linearprogrammingrelaxation and a technique called iterative, randomized rounding. The general...
branch-and-bound where every subproblem is solved by constructing a linearprogrammingrelaxation to obtain a lower bound. Branching may occur at both continuous...
generalized assignment problem is NP-hard, However, there are linear-programmingrelaxations which give a ( 1 − 1 / e ) {\displaystyle (1-1/e)} -approximation...
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