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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 ..."
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Cited by 39 (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.
Logicbased Modeling and Solution of Nonlinear Discrete/Continuous Optimization Problems
"... This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are modeled with algebraic equations and inequalities. Since algebraic representations ha ..."
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Cited by 9 (6 self)
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This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are modeled with algebraic equations and inequalities. Since algebraic representations have some limitations such as difficulty of formulation and numerical singularities for the nonlinear case, we consider logicbased modeling as an alternative approach, particularly Generalized Disjunctive Programming (GDP), which the authors have extensively investigated over the last few years. Solution strategies for GDP models are reviewed, including the continuous relaxation of the disjunctive constraints. Also, we briefly review a hybrid model that integrates disjunctive programming and mixed integer programming. Finally, the global optimization of nonconvex GDP problems is discussed through a twolevel branch and bound procedure.
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.
Optimization
, 2006
"... This paper presents two novel formulations for solving the sequence selection problem in de novo protein design with highly flexible templates, each of which exhibits a crystal or NMR structure. The first formulation applies weighted average energy parameters to incorporate information about every s ..."
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This paper presents two novel formulations for solving the sequence selection problem in de novo protein design with highly flexible templates, each of which exhibits a crystal or NMR structure. The first formulation applies weighted average energy parameters to incorporate information about every structure, with the weights, which are parameters dependent on a pair of C α positions and a particular distance bin, given by the probability that the distance between the two positions is found to belong to that distance bin in any of the structures. The second formulation allows the distance between the two positions considered to fall into any distance bin that all the structures span over, but imposes novel linear constraints to ensure a physically consistent structure. Both formulations were tested on redesigning Compstatin, the template of which has 21 NMR structures from the
CHAPTER 11 ADVANCES IN LOGICBASED OPTIMIZATION APPROACHES TO PROCESS INTEGRATION AND SUPPLY CHAIN MANAGEMENT
"... Abstract. Optimization as an enabling technology has been one of the big success stories in process systems engineering. In this paper we present a review on recent research work in the area of logicbased discrete/continuous optimization. In particular, recent advances are presented in the modeling ..."
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Abstract. Optimization as an enabling technology has been one of the big success stories in process systems engineering. In this paper we present a review on recent research work in the area of logicbased discrete/continuous optimization. In particular, recent advances are presented in the modeling and solution of nonlinear mixedinteger and generalized disjunctive programming, global optimization and constraint programming. The impact of these techniques is illustrated with several examples in the areas of process integration and supply chain management.. Our objective in this chapter is to provide an overview of new developments in discrete/continuous optimization with applications to process integration and supply chain management problems. The emphasis is on logicbased optimization which is becoming a new promising area in process systems engineering.