A proximal-point outer approximation algorithm

Many engineering and scientific applications, e.g. resource allocation, control of hybrid systems, scheduling, etc., require the solution of mixed-integer non-linear problems (MINLPs). Problems of such class combine the high computational burden arising from considering discrete variables with the c...

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Vydáno v:Computational optimization and applications Ročník 77; číslo 3; s. 755 - 777
Hlavní autoři: De Mauri, Massimo, Gillis, Joris, Swevers, Jan, Pipeleers, Goele
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.12.2020
Springer Nature B.V
Témata:
Algorithms
Approximation
Convex and Discrete Geometry
Feasibility
Heuristic methods
Hybrid systems
Linear functions
Linear programming
Management Science
Mathematics
Mathematics and Statistics
Mixed integer
Nonlinear programming
Operations Research
Operations Research/Decision Theory
Optimization
Resource allocation
Statistics
Linear outer approximation
Mixed-integer programming
Feasibility pump
Mixed-integer non-linear optimization
ISSN:0926-6003, 1573-2894
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Shrnutí:Many engineering and scientific applications, e.g. resource allocation, control of hybrid systems, scheduling, etc., require the solution of mixed-integer non-linear problems (MINLPs). Problems of such class combine the high computational burden arising from considering discrete variables with the complexity of non-linear functions. As a consequence, the development of algorithms able to efficiently solve medium-large MINLPs is still an interesting field of research. In the last decades, several approaches to tackle MINLPs have been developed. Some of such approaches, usually defined as exact methods, aim at finding a globally optimal solution for a given MINLP at expense of a long execution time, while others, generally defined as heuristics, aim at discovering suboptimal feasible solutions in the shortest time possible. Among the various proposed paradigms, outer approximation (OA) and feasibility pump (FP), respectively as exact method and as heuristic, deserve a special mention for the number of relevant publications and successful implementations related to them. In this paper we present a new exact method for convex mixed-integer non-linear programming called proximal outer approximation (POA). POA blends the fundamental ideas behind FP into the general OA scheme that attepts to yield faster and more robust convergence with respect to OA while retaining the good performances in terms of fast generation of feasible solutions of FP.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-020-00216-9