A general system for heuristic minimization of convex functions over non-convex sets. We describe general heuristics to approximately solve a wide variety of problems with convex objective and decision variables from a non-convex set. The heuristics, which employ convex relaxations, convex restrictions, local neighbour search methods, and the alternating direction method of multipliers, require the solution of a modest number of convex problems, and are meant to apply to general problems, without much tuning. We describe an implementation of these methods in a package called NCVX, as an extension of CVXPY, a Python package for formulating and solving convex optimization problems. We study several examples of well known non-convex problems, and show that our general purpose heuristics are effective in finding approximate solutions to a wide variety of problems.
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References in zbMATH (referenced in 3 articles )
Showing results 1 to 3 of 3.
- Pecci, Filippo; Abraham, Edo; Stoianov, Ivan: Global optimality bounds for the placement of control valves in water supply networks (2019)
- Diamond, S.; Takapoui, R.; Boyd, S.: A general system for heuristic minimization of convex functions over non-convex sets (2018)
- Kanno, Yoshihiro; Fujita, Shinnosuke: Alternating direction method of multipliers for truss topology optimization with limited number of nodes: a cardinality-constrained second-order cone programming approach (2018)