Algorithms for discrete nonlinear optimization in FICO Xpress

The FICO Xpress-Optimizer is a commercial optimization solver for linear programming (LP), mixed integer linear programming (MIP), convex quadratic programming (QP), convex quadratically constrained quadratic programming (QCQP), second-order cone programming (SOCP) and their mixed-integer counterparts. Xpress also includes a general purpose non-linear solver, Xpress-NonLinear, which features a successive linear programming algorithm (SLP, first-order method), interior point methods and Artelys Knitro (second-order methods). This work explores algorithms for mixed-integer nonlinear programming problems (MINLPs), which are NP-hard in general, then it presents applications in signal processing and capitalizes advances in solving these problems with Xpress and its comprehensive suite of high-performance nonlinear solvers. Computational results show that signal processing nonlinear problems can be solved quickly and accurately, taking advantage of the algebraic modeling and procedural programming language, Xpress-Mosel, that allows to interact with the Xpress solver engines in a easy-to-learn way, and its unified modeling interface for all solvers, from linear to general nonlinear solvers.