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Solving nonconvex nonlinear programs with reverse convex constraints by sequential linear programming
Author(s) -
Drezner Zvi,
Kalczynski Pawel
Publication year - 2020
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12736
Subject(s) - mathematical optimization , nonlinear programming , convergence (economics) , linear programming , nonlinear system , computer science , local optimum , regular polygon , convex optimization , sequence (biology) , mathematics , physics , geometry , quantum mechanics , biology , economics , genetics , economic growth
The sequential linear programming (SLP) method for solving nonlinear problems was introduced in the 1960s. Many papers that attempted to use SLP reported poor performance and convergence issues. We found that nonlinear programs with reverse convex constraints, which are the most difficult nonlinear programs with many local optima, are solved (heuristically) very well by SLP. We proved that for this type of problems, the solutions to the sequence of the linear programming problems converge to a local optimum. Since the final solution depends on the starting solution, we propose to apply SLP in a multistart approach starting from randomly generated solutions. This multistart SLP is very easy to implement. We recommend that the research community reconsiders the application of SLP for this type of problems.