‎In this paper‎, ‎some KKT type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (MINPP) are established‎. ‎We achieve‎ ‎this by employing a Lagrange function for MINPP‎. ‎In addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...

Global optimization of mixed-integer nonlinear bilevel optimization problems is addressed using a novel technique. For problems where integer variables participate in both inner and outer problems, the outer level may involve general mixed-integer nonlinear functions. The inner level may involve functions that are mixed-integer nonlinear in outer variables, linear, polynomial, or multilinear in...

In this contribution we apply different approaches to solve four rather different MINLP problems: special extensions to time-indexed formulations of production planning problems, a production planning problem in BASF’s petrochemical division, a site analysis of one of BASF’s bigger sites, and a process design problem. The first problem is related to a useful nonlinear extension of production pl...

This manuscript introduces ANTIGONE, Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations, a general mixed-integer nonlinear global optimization framework. ANTIGONE is the evolution of the Global Mixed-Integer Quadratic Optimizer, GloMIQO, to general nonconvex terms. The purpose of this paper is to show how the extensible structure of ANTIGONE realizes our previously-p...

We propose a decomposition algorithm for a special class of nonconvex mixed integer nonlinear programming problems which have an assignment constraint. If the assignment decisions are decoupled from the remaining constraints of the optimization problem, we propose to use a column enumeration approach. The master problem is a partitioning problem whose objective function coefficients are compute...

Abstract Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification nonlinear dynamics (SINDy) framework, powered by heuristic regression methods, has become dominant tool for learning parsimonious models. We propose an exact formulation SINDy using mixed-integer optimization (MI...

Abstract Currently, few approaches are available for mixed-integer nonlinear robust optimization. Those that do exist typically either require restrictive assumptions on the problem structure or not guarantee protection. In this work, we develop an algorithm convex optimization problems where a key feature is method does rely specific of inner worst-case (adversarial) and allows latter to be no...

Mixed-integer nonlinear optimization problems arise in scientific and operational applications ranging from the reordering of nuclear fuel rods to the design of wireless networks. We present some novel mixed-integer nonlinear optimization applications and review existing solution techniques. We also describe some experiments with nonlinear branch-and-bound branching techniques that lead us to p...