A multiplicative weights update algorithm for MINLP

Abstract

We discuss an application of the well-known multiplicative weights update (MWU) algorithm to non-convex and mixed-integer non-linear programming. We present applications to: (a) the distance geometry problem, which arises in the positioning of mobile sensors and in protein conformation; (b) a hydro unit commitment problem arising in the energy industry, and (c) a class of Markowitz’ portfolio selection problems. The interest of the MWU with respect to one of its closest competitors (classic multi-start) is that it provides a relative approximation guarantee on a certain quality measure of the solution.

Keywords

• Mixed Integer Nonlinear Programming (MINLP)
• Multiplicative Weights Update (MWU)
• MWU Algorithm
• Distance Geometry Problem (DGP)
• Unit Commitment Problem