author={C. D'Ambrosio and Jon Lee and A. W{\"a}chter},
We present an algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems in which the non-convexity in the objective and constraint functions is manifested as the sum of non-convex univariate functions. We employ a lower bounding convex MINLP relaxation obtained by approximating each non-convex function with a piecewise-convex underestimator that is repeatedly refined. The algorithm is implemented at the level of a modeling language. Favorable numerical results are presented. 
Non-convex mixed-integer nonlinear programming: A survey
Abstract A wide range of problems arising in practical applications can be formulated as Mixed-Integer Nonlinear Programs (MINLPs). For the case in which the objective and constraint functions areExpand
Strengthening the sequential convex MINLP technique by perspective reformulations
This work proposes to modify the convex terms using the Perspective Reformulation technique to strengthen the bounds of the sequential convex MINLP, and shows by means of experimental results that doing so significantly decreases the solution time of the conveX MINLPs. Expand
On global optimization with indefinite quadratics
An algorithmic framework for global optimization problems in which the non-convexity is manifested as an indefinite-quadratic as part of the objective function and several natural possibilities for splitting an indefinite quadratic at the preprocessing stage are investigated, and the equivalence of some of them is proved. Expand
Handling Separable Non-convexities Using Disjunctive Cuts
This work proposes a method for addressing the same setting, but employing disjunctive cuts (generated via LP), and solving instead a sequence of convex NLPs, and presents computational results which demonstrate the viability of this approach. Expand
Valid inequalities for separable concave constraints with indicator variables
This work proposes a technique to obtain valid inequalities that are based on both the MILP constraints and the concave constraints and presents computational results demonstrating the utility of the new inequalities for nonlinear transportation problems and for lot-sizing problems with concave costs. Expand
Valid Inequalities for Separable Concave Constraints with Indicator Variables
This is one of the first works that simultaneously convexifies both nonconvex functions and binary variables to strengthen the relaxations of practical mixed integer nonlinear programs. Expand
Application-oriented mixed integer non-linear programming
The main topic of the thesis is Mixed Integer Non-Linear Programming, with focus on non-convex problems and real-world applications and different kinds of algorithms are presented: linearization methods, heuristic and global optimization algorithms. Expand
Maximizing a Sum of Sigmoids
The problem of maximizing a sum of sigmoidal functions over a convex constraint set arises in many application areas. This objective captures the idea of decreasing marginal returns to investment,Expand
Techniques for Submodular Maximization
Maximization of a submodular function is a central problem in the algorithmic theory of combinatorial optimization and novel branch-and-bound methods have proven to be effective on broad subclasses of problems. Expand
Discrete geometry and optimization
Preface.- Discrete Geometry in Minkowski Spaces (Alonso, Martini, and Spirova).- Engineering Branch-and-Cut Algorithms for the Equicut Program (Anjos, Liers, Pardella, and Schmutzer).- An Approach toExpand


A Global-Optimization Algorithm for Mixed-Integer Nonlinear Programs Having Separable Non-convexity
We present a global optimization algorithm for MINLPs (mixed-integer nonlinear programs) where any non-convexity is manifested as sums of non-convex univariate functions. The algorithm is implementedExpand
LaGO - An Object Oriented Library for Solving MINLPs
The paper describes a software package called LaGO for solving nonconvex mixed integer nonlinear programs (MINLPs). The main component of LaGO is a convex relaxation which is used for generatingExpand
IBM Research Report MINLP Strengthening for Separable Convex Quadratic Transportation-Cost UFL
A disaggregation principal and a strategy of developing model-specific valid inequalities enable us to significantly improve the quality of the NLP (Nonlinear Programming) relaxation of the authors' MINLP model. Expand
An algorithmic framework for convex mixed integer nonlinear programs
A class of hybrid algorithms, of which branch-and-bound and polyhedral outer approximation are the two extreme cases, are proposed and implemented and Computational results that demonstrate the effectiveness of this framework are reported. Expand
Solving mixed integer nonlinear programs by outer approximation
An alternative approach is considered to the difficulties caused by infeasibility in outer approximation, in which exact penalty functions are used to solve the NLP subproblems. Expand
Optimization under Composite Monotonic Constraints and Constrained Optimization over the Efficient Set
The approach is based on transforming the problem into a monotonic optimization problem in the space ℝp, which can then be efficiently solved by recently developed techniques. Expand
Branching and bounds tighteningtechniques for non-convex MINLP
An sBB software package named couenne (Convex Over- and Under-ENvelopes for Non-linear Estimation) is developed and used for extensive tests on several combinations of BT and branching techniques on a set of publicly available and real-world MINLP instances and is compared with a state-of-the-art MINLP solver. Expand
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
A comprehensive description of the primal-dual interior-point algorithm with a filter line-search method for nonlinear programming is provided, including the feasibility restoration phase for the filter method, second-order corrections, and inertia correction of the KKT matrix. Expand
BARON: A general purpose global optimization software package
  • N. Sahinidis
  • Mathematics, Computer Science
  • J. Glob. Optim.
  • 1996
The Branch-And-Reduce Optimization Navigator (BARON) is a computational system for facilitating the solution of nonconvex optimization problems to global optimality. We provide a brief description ofExpand
An LP/NLP based branch and bound algorithm for convex MINLP optimization problems
Abstract This paper is aimed at improving the solution efficiency of convex MINLP problems in which the bottleneck lies in the combinatorial search for the 0–1 variables. An LP/NLP based branch andExpand