# MIPNLP

### From TomWiki

# Overview

Welcome to the TOMLAB /MIPNLP User's Guide. TOMLAB /MIPNLP includes four solvers for mixed integer programming problems. The solvers take advantage of the wide array of subsolvers for LP, NLP and MILP in TOMLAB.

The solver package includes the following solvers:

ecpMINLP - Solves convex or pseudo-convex mixed-integer nonlinear programming problems using an extended cutting plane algorithm with cuts regulated by a parameter-vector alpha. Cuts and linearizations are added to a MIP subproblem solved by a subsolver in each iteration. The solver algorithm is an implementation based on the publication 'Solving Pseudo-Convex Mixed Integer Optimization Problems by Cutting Plane Techniques' by Tapio Westerlund and Ray Pörn, Optimization and Engineering 3, 253-280, 2002, but with modifications.

stoaMINLP - Single-search Tree Outer Approximation Solver for Mixed-Integer NonLinear Programming (MINLP). Is best suited for solving convex problems. The solver is mainly based on 'FilMINT: An Outer-Approximation-Based Solver for Nonlinear Mixed Integer Programs' by Kumar Abhishek, Sven Leyffer, and Jeffrey T. Linderoth at the Mathematics and Computer Science Division, Preprint ANL/MCS-P1374-0906, March 28, 2008, but with some differences.