22 Result(s)
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Article
BARON: A general purpose global optimization software package
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 of the algor...
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A branch-and-reduce approach to global optimization
This paper presents valid inequalities and range contraction techniques that can be used to reduce the size of the search space of global optimization problems. To demonstrate the algorithmic usefulness of the...
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A Finite Algorithm for Global Minimization of Separable Concave Programs
Researchers first examined the problem of separable concave programming more than thirty years ago, making it one of the earliest branches of nonlinear programming to be explored. This paper proposes a new alg...
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Article
Analysis of Bounds for Multilinear Functions
We analyze four bounding schemes for multilinear functions and theoretically compare their tightness. We prove that one of the four schemes provides the convex envelope and that two schemes provide the concave...
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Article
Semidefinite Relaxations of Fractional Programs via Novel Convexification Techniques
In a recent work, we introduced the concept of convex extensions for lower semi-continuous functions and studied their properties. In this work, we present new techniques for constructing convex and concave en...
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Article
Global Optimization of 0-1 Hyperbolic Programs
We develop eight different mixed-integer convex programming reformulations of 0-1 hyperbolic programs. We obtain analytical results on the relative tightness of these formulations and propose a branch and boun...
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Global Optimization of Multiplicative Programs
This paper develops global optimization algorithms for linear multiplicative and generalized linear multiplicative programs based upon the lower bounding procedure of Ryoo and Sahinidis [30] and new greedy bra...
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Accelerating Branch-and-Bound through a Modeling Language Construct for Relaxation-Specific Constraints
In the tradition of modeling languages for optimization, a single model is passed to a solver for solution. In this paper, we extend BARON’s modeling language in order to facilitate the communication of proble...
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Article
Global optimization in stabilizing controller design
In this paper, we develop a global optimization methodology to solve stabilization problems. We first formulate stabilization problems as bilevel programming problems. By invoking the Hurwitz stability conditi...
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Convex envelopes of products of convex and component-wise concave functions
In this paper, we consider functions of the form \({\phi(x,y)=f(x)g(y)}\) over a box, where
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Article
Open AccessDerivative-free optimization: a review of algorithms and comparison of software implementations
This paper addresses the solution of bound-constrained optimization problems using algorithms that require only the availability of objective function values but no derivative information. We refer to these al...
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Article
Preface: Honoring the 60th birthday of Panos M. Pardalos
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Article
Global optimization of general nonconvex problems with intermediate polynomial substructures
This work considers the global optimization of general nonconvex nonlinear and mixed-integer nonlinear programming problems with underlying polynomial substructures. We incorporate linear cutting planes inspir...
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Bounds tightening based on optimality conditions for nonconvex box-constrained optimization
First-order optimality conditions have been extensively studied for the development of algorithms for identifying locally optimal solutions. In this work, we propose two novel methods that directly exploit the...
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Article
An efficient strategy for the activation of MIP relaxations in a multicore global MINLP solver
Solving mixed-integer nonlinear programming (MINLP) problems to optimality is a NP-hard problem, for which many deterministic global optimization algorithms and solvers have been recently developed. MINLPs can...
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Global optimization of nonconvex problems with convex-transformable intermediates
This paper addresses the global optimization of problems which contain convex-transformable functions. We present algorithms for identification of convex-transformable functions in general nonconvex problems, ...
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Tuning BARON using derivative-free optimization algorithms
Optimization solvers include many options that allow users to control algorithmic aspects that may have a considerable impact on solver performance. Tuning solver options is often necessary to reduce execution...
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Article
Optimality-based domain reduction for inequality-constrained NLP and MINLP problems
In spatial branch-and-bound algorithms, optimality-based domain reduction is normally performed after solving a node and relies on duality information to reduce ranges of variables. In this work, we propose no...
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Article
Backward Stepwise Elimination: Approximation Guarantee, a Batched GPU Algorithm, and Empirical Investigation
Best subset selection is NP-hard and expensive to solve exactly for problems with a large number of features. Practitioners often employ heuristics to quickly obtain approximate solutions without any accuracy ...
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Article
Decomposition in derivative-free optimization
This paper proposes a novel decomposition framework for derivative-free optimization (DFO) algorithms. Our framework significantly extends the scope of current DFO solvers to larger-scale problems. We show tha...
