-
Article
Open AccessThe supporting hyperplane optimization toolkit for convex MINLP
In this paper, an open-source solver for mixed-integer nonlinear programming (MINLP) problems is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) combines a dual strategy based on polyhedral ou...
-
Article
Open AccessPolyhedral approximation strategies for nonconvex mixed-integer nonlinear programming in SHOT
Different versions of polyhedral outer approximation are used by many algorithms for mixed-integer nonlinear programming (MINLP). While it has been demonstrated that such methods work well for convex MINLP, ex...
-
Chapter and Conference Paper
On Solving Nonconvex MINLP Problems with SHOT
The Supporting Hyperplane Optimization Toolkit (SHOT) solver was originally developed for solving convex MINLP problems, for which it has proven to be very efficient. In this paper, we describe some techniques...
-
Article
Open AccessA review and comparison of solvers for convex MINLP
In this paper, we present a review of deterministic software for solving convex MINLP problems as well as a comprehensive comparison of a large selection of commonly available solvers. As a test set, we have u...
-
Article
Reformulations for utilizing separability when solving convex MINLP problems
Several deterministic methods for convex mixed integer nonlinear programming generate a polyhedral approximation of the feasible region, and utilize this approximation to obtain trial solutions. Such methods a...
-
Article
The extended supporting hyperplane algorithm for convex mixed-integer nonlinear programming
A new deterministic algorithm for solving convex mixed-integer nonlinear programming (MINLP) problems is presented in this paper: The extended supporting hyperplane (ESH) algorithm uses supporting hyperplanes ...
-
Article
A reformulation framework for global optimization
In this paper, we present a global optimization method for solving nonconvex mixed integer nonlinear programming (MINLP) problems. A convex overestimation of the feasible region is obtained by replacing the no...
-
Chapter and Conference Paper
Improved Discrete Reformulations for the Quadratic Assignment Problem
This paper presents an improved as well as a completely new version of a mixed integer linear programming (MILP) formulation for solving the quadratic assignment problem (QAP) to global optimum. Both formulati...
-
Chapter and Conference Paper
Global Optimization of Mixed-Integer Signomial Programming Problems
Described in this chapter, is a global optimization algorithm for mixedinteger nonlinear programming problems containing signomial functions. The method obtains a convex relaxation of the nonconvex problem thr...
-
Article
Some transformation techniques with applications in global optimization
In this paper some transformation techniques, based on power transformations, are discussed. The techniques can be applied to solve optimization problems including signomial functions to global optimality. Sig...
