3 research outputs found
Convexification of Queueing Formulas by Mixed-Integer Second-Order Cone Programming: An Application to a Discrete Location Problem with Congestion
Mixed-Integer Second-Order Cone Programs (MISOCPs) form a nice class of
mixed-inter convex programs, which can be solved very efficiently due to the
recent advances in optimization solvers. Our paper bridges the gap between
modeling a class of optimization problems and using MISOCP solvers. It is shown
how various performance metrics of M/G/1 queues can be molded by different
MISOCPs. To motivate our method practically, it is first applied to a
challenging stochastic location problem with congestion, which is broadly used
to design socially optimal service networks. Four different MISOCPs are
developed and compared on sets of benchmark test problems. The new formulations
efficiently solve large-size test problems, which cannot be solved by the best
existing method. Then, the general applicability of our method is shown for
similar optimization problems that use queue-theoretic performance measures to
address customer satisfaction and service quality
A comparative note on the relaxation algorithms for the linear semi-infinite feasibility problem
The problem (LFP) of finding a feasible solution to a given linear semi-infinite system arises in different contexts. This paper provides an empirical comparative study of relaxation algorithms for (LFP). In this study we consider, together with the classical algorithm, implemented with different values of the fixed parameter (the step size), a new relaxation algorithm with random parameter which outperforms the classical one in most test problems whatever fixed parameter is taken. This new algorithm converges geometrically to a feasible solution under mild conditions. The relaxation algorithms under comparison have been implemented using the extended cutting angle method for solving the global optimization subproblems.This research was partially supported by MICINN of Spain, Grant MTM2014-59179-C2-1-P and Sistema Nacional de Investigadores, Mexico
On Chubanov's method for Linear Programming
We discuss the method recently proposed by S. Chubanov for the linear feasibility
problem. We present new, concise proofs and interpretations of some of his results. We then
show how our proofs can be used to find strongly polynomial time algorithms for special
classes of linear feasibility problems. Under certain conditions, these results provide new
proofs of classical results obtained by Tardos, and Vavasis and Ye