Abstract
An efficient active-set approach is presented for both nonnegative and general linear programming by adding varying numbers of constraints at each iteration. Computational experiments demonstrate that the proposed approach is significantly faster than previous active-set and standard linear programming algorithms.
Highlights
IntroductionThe non-polynomial simplex methods and polynomial interior-point barrier-function algorithms illustrate the two different approaches to solve problem P
Consider the linear programming problem (P) Max z = cT x (1) s.t
CPU times for constraint optimal selection technique (COST) GRAD and VIOL using both the multi-cut technique and dynamic approaches are presented for comparison
Summary
The non-polynomial simplex methods and polynomial interior-point barrier-function algorithms illustrate the two different approaches to solve problem P. Interior point methods do not provide efficient post-optimality analysis, so the simplex algorithm is the most frequently used approach [2], even for sparse large scale linear programming problems where barrier methods perform extremely well. We propose active-set methods for LPs and NNLPs. Our approach divides the constraints of problem P into operative and inoperative constraints at each iteration. Multiple violated constraints are added to problems Pr, r = 0,1, , according to the constraint selection metric RAD or GRAD.
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