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14
Complete search in continuous global optimization and constraint satisfaction, Acta Numerica 13
, 2004
"... A chapter for ..."
Interval Analysis on Directed Acyclic Graphs for Global Optimization
 J. Global Optimization
, 2004
"... A directed acyclic graph (DAG) representation of optimization problems represents each variable, each operation, and each constraint in the problem formulation by a node of the DAG, with edges representing the ow of the computation. ..."
Abstract

Cited by 40 (8 self)
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A directed acyclic graph (DAG) representation of optimization problems represents each variable, each operation, and each constraint in the problem formulation by a node of the DAG, with edges representing the ow of the computation.
Global minimization using an Augmented Lagrangian method with variable lowerlevel constraints
, 2007
"... A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the εkglobal minimization of the Augmented Lagrangian with simple constraints, where εk → ε. Global c ..."
Abstract

Cited by 21 (1 self)
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A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration k the method requires the εkglobal minimization of the Augmented Lagrangian with simple constraints, where εk → ε. Global convergence to an εglobal minimizer of the original problem is proved. The subproblems are solved using the αBB method. Numerical experiments are presented.
Reformulations in Mathematical Programming: A Computational Approach
"... Summary. Mathematical programming is a language for describing optimization problems; it is based on parameters, decision variables, objective function(s) subject to various types of constraints. The present treatment is concerned with the case when objective(s) and constraints are algebraic mathema ..."
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Cited by 17 (13 self)
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Summary. Mathematical programming is a language for describing optimization problems; it is based on parameters, decision variables, objective function(s) subject to various types of constraints. The present treatment is concerned with the case when objective(s) and constraints are algebraic mathematical expressions of the parameters and decision variables, and therefore excludes optimization of blackbox functions. A reformulation of a mathematical program P is a mathematical program Q obtained from P via symbolic transformations applied to the sets of variables, objectives and constraints. We present a survey of existing reformulations interpreted along these lines, some example applications, and describe the implementation of a software framework for reformulation and optimization. 1
On convex relaxations for quadratically constrained quadratic programming
 Mathematical Programming (Series B
, 2012
"... We consider convex relaxations for the problem of minimizing a (possibly nonconvex) quadratic objective subject to linear and (possibly nonconvex) quadratic constraints. Let F denote the feasible region for the linear constraints. We first show that replacing the quadratic objective and constraint f ..."
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Cited by 2 (0 self)
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We consider convex relaxations for the problem of minimizing a (possibly nonconvex) quadratic objective subject to linear and (possibly nonconvex) quadratic constraints. Let F denote the feasible region for the linear constraints. We first show that replacing the quadratic objective and constraint functions with their convex lower envelopes on F is dominated by an alternative methodology based on convexifying the range of the quadratic form () () 1 1 T x x for x ∈ F. We next show that the use of “αBB” underestimators as computable estimates of convex lower envelopes is dominated by a relaxation of the convex hull of the quadratic form that imposes semidefiniteness and linear constraints on diagonal terms. Finally, we show that the use of a large class of “D.C. ” underestimators is dominated by a relaxation that combines semidefiniteness with RLT constraints.
Computational Methods for Protein Fold Prediction: an Abinitio Topological Approach
"... Summary. The prediction of protein native conformations is still a big challenge in science, although a strong research activity has been carried out on this topic in the last decades. In this chapter we focus on abinitio computational methods for protein fold predictions that do not rely heavily o ..."
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Cited by 1 (1 self)
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Summary. The prediction of protein native conformations is still a big challenge in science, although a strong research activity has been carried out on this topic in the last decades. In this chapter we focus on abinitio computational methods for protein fold predictions that do not rely heavily on comparisons with known protein structures and hence appear to be the most promising methods for determining conformations not yet been observed experimentally. To identify main trends in the research concerning protein fold predictions, we briefly review several abinitio methods, including a recent topological approach that models the protein conformation as a tube having maximum thickness without any selfcontacts. This representation leads to a constrained global optimization problem. We introduce a modification in the tube model to increase the compactness of the computed conformations, and present results of computational experiments devoted to simulating αhelices and allα proteins. A Metropolis Monte Carlo Simulated Annealing algorithm is used to search the protein conformational space.
Global optimization of robust chance constrained problems
, 2007
"... We propose a stochastic algorithm for the global optimization of chance constrained problems. We assume that the probability measure with which the constraints are evaluated is known only through its moments. The algorithm proceeds in two phases. In the first phase the probability distribution is (c ..."
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We propose a stochastic algorithm for the global optimization of chance constrained problems. We assume that the probability measure with which the constraints are evaluated is known only through its moments. The algorithm proceeds in two phases. In the first phase the probability distribution is (coarsely) discretized and solved to global optimality using a stochastic algorithm. We only assume that the stochastic algorithm exhibits a weak * convergence to a probability measure assigning all its mass to the discretized problem. A diffusion process is derived that has this convergence property. In the second phase, the discretization is improved by solving another nonlinear programming problem. It is shown that the algorithm converges to the solution of the original problem. We discuss the numerical performance of the algorithm and its application to process design. 1
MINLP Solver Software
, 2010
"... In this article we will give a brief overview of the startoftheart on software for the solution of mixed integer nonlinear programs (MINLP). We establish several groupings with respect to various features and give concise individual descriptions for each solver. ..."
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In this article we will give a brief overview of the startoftheart on software for the solution of mixed integer nonlinear programs (MINLP). We establish several groupings with respect to various features and give concise individual descriptions for each solver.
Deterministic and stochastic global optimization techniques for planar covering with ellipses problems ∗
, 2011
"... Problems of planar covering with ellipses are tackled in this work. Ellipses can have a fixed angle or each of them can be freely rotated. Deterministic global optimization methods are developed for both cases, while a stochastic version of the method is also proposed for large instances of the latt ..."
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Problems of planar covering with ellipses are tackled in this work. Ellipses can have a fixed angle or each of them can be freely rotated. Deterministic global optimization methods are developed for both cases, while a stochastic version of the method is also proposed for large instances of the latter case. Numerical results show the effectiveness and efficiency of the proposed methods. Key words: Planar covering with ellipses, deterministic global optimization, algorithms.
investigations. A Branch and Bound Algorithm for the Global Optimization of Hessian Lipschitz Continuous Functions
, 1358
"... the global optimization of Hessian ..."