mixed integer nonlinear programming

[...]... techniques for solving Mixed Integer Linear Programs and incorporating these techniques into software, significant improvements have been made in the ability to solve these problems Key words Mixed Integer Nonlinear Programming; Branch and Bound 1 Introduction Mixed- Integer Nonlinear Programs (MINLP)s are optimization problems where some of the variables are constrained to take integer values and the... Part VIII: Complexity On the complexity of nonlinear mixed- integer optimization 533 Matthias K¨ppe o Theory and applications of n-fold integer programming 559 Shmuel Onn CONTENTS xvii Part IX: Applications MINLP Application for ACH interiors restructuring 597 Erica Klampfl and Yakov Fradkin A benchmark library of mixed- integer optimal control problems 631... of nonlinear mixed- integer optimization (M K¨ppe) o is a survey on the computational complexity of MINLP It includes incomputability results that arise from number theory and logic, fully polynomialtime approximation schemes in fixed dimension, and polynomial-time algorithms for special cases Theory and applications of n-fold integer programming (S Onn) is an overview of the theory of n-fold integer programming, ... optimizing over integer variables with the handling of nonlinear functions Even if we restrict our model to contain only linear functions, MINLP reduces to a Mixed- Integer Linear Program (MILP), which is an NP-Hard problem [55] On the other hand, if we restrict our model to have no integer variable but allow for general nonlinear functions in the objective or the constraints, then MINLP reduces to a Nonlinear. .. problems A global-optimization algorithm for mixed- integer nonlinear programs having separable nonconvexity (C D’Ambrosio, J Lee, and A W¨chter) a introduces a method for MINLPs that have all of their nonconvexity in separable form The approach aims to retain and exploit existing convexity in the formulation Global optimization of mixed- integer signomial programming problems (A Lundell and T Westerlund)... participants 671 PART I: Convex MINLP ALGORITHMS AND SOFTWARE FOR CONVEX MIXED INTEGER NONLINEAR PROGRAMS PIERRE BONAMI∗ , MUSTAFA KILINC† , AND JEFF LINDEROTH‡ ¸ Abstract This paper provides a survey of recent progress and software for solving convex Mixed Integer Nonlinear Programs (MINLP)s, where the objective and constraints are defined by convex functions and integrality... vii Part I: Convex MINLP Algorithms and software for convex mixed integer nonlinear programs 1 Pierre Bonami, Mustafa Kilin¸, and Jeff Linderoth c Subgradient based outer approximation for mixed integer second order cone programming 41 Sarah Drewes and Stefan Ulbrich... and Andreas W¨chter a Global optimization of mixed- integer signomial programming problems 349 Andreas Lundell and Tapio Westerlund Part VI: Mixed- Integer Quadraticaly Constrained Optimization The MILP road to MIQCP 373 Samuel Burer and Anureet Saxena Linear programming relaxations of quadratically constrained... Gill and Elizabeth Wong Using interior-point methods within an outer approximation framework for mixed integer nonlinear programming 225 Hande Y Benson Part IV: Expression Graphs Using expression graphs in optimization algorithms 247 David M Gay Symmetry in mathematical programming 263 Leo Liberti xv xvi CONTENTS Part V: Convexification... surveys results in mixed- integer quadratically constrained programming Strong convex relaxations and valid inequalities are the basis of efficient, practical techniques for global optimization Some of the relaxations and inequalities are derived from the algebraic formulation, while others are based on disjunctive programming Much of the inspiration derives from MILP methodology Linear programming relaxations . Mathematics and its Applications MIXED INTEGER NONLINEAR PROGRAMMING contains expository and research papers based on a highly successful IMA Hot Topics Workshop Mixed- Integer Nonlinear Optimization:. n-fold integer programming (S. Onn) is an overview of the theory of n-fold integer programming, which enables the polynomial-time solution of fundamental linear and nonlinear inte- ger programming. software for convex mixed integer nonlinear programs 1 Pierre Bonami, Mustafa Kilin¸c, and Jeff Linderoth Subgradient based outer approximation for mixed integer second ordercone programming 41 Sarah