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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 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.
Towards Implementations of Successive Convex Relaxation Methods for Nonconvex Quadratic Optimization Problems
, 1999
"... Recently Kojima and Tuncel proposed new successive convex relaxation methods and their localizeddiscretized variants for general nonconvex quadratic optimization problems. Although an upper bound of the optimal objective function value within a previously given precision can be found theoretically ..."
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Cited by 12 (6 self)
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Recently Kojima and Tuncel proposed new successive convex relaxation methods and their localizeddiscretized variants for general nonconvex quadratic optimization problems. Although an upper bound of the optimal objective function value within a previously given precision can be found theoretically by solving a finite number of linear programs, several important implementation issues remain unsolved. In this paper, we discuss those issues, present practically implementable algorithms and report numerical results.
Deterministic Global Optimization In Design, Control, And Computational Chemistry
 IMA Volumes in Mathematics and its Applications : Large Scale Optimization with Applications, Part II
, 1997
"... . This paper presents an overview of the deterministic global optimization approaches and their applications in the areas of Process Design, Control, and Computational Chemistry. The focus is on (i) decompositionbased primal dual methods, (ii) methods for generalized geometric programming problems, ..."
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Cited by 10 (7 self)
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. This paper presents an overview of the deterministic global optimization approaches and their applications in the areas of Process Design, Control, and Computational Chemistry. The focus is on (i) decompositionbased primal dual methods, (ii) methods for generalized geometric programming problems, and (iii) global optimization methods for general nonlinear programming problems. The classes of mathematical problems that are addressed range from indefinite quadratic programming to concave programs, to quadratically constrained problems, to polynomials, to general twice continuously differentiable nonlinear optimization problems. For the majority of the presented methods nondistributed global optimization approaches are discussed with the exception of decompositionbased methods where a distributed global optimization approach is presented. 1. Background. A significant effort has been expended in the last five decades toward theoretical and algorithmic studies of applications that arise...
Global Optimization of Nonconvex Nonlinear Programs Using Parallel Branch and Bound
, 1995
"... A branch and bound algorithm for computing globally optimal solutions to nonconvex nonlinear programs in continuous variables is presented. The algorithm is directly suitable for a wide class of problems arising in chemical engineering design. It can solve problems defined using algebraic functions ..."
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Cited by 8 (0 self)
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A branch and bound algorithm for computing globally optimal solutions to nonconvex nonlinear programs in continuous variables is presented. The algorithm is directly suitable for a wide class of problems arising in chemical engineering design. It can solve problems defined using algebraic functions and twice differentiable transcendental functions, in which finite upper and lower bounds can be placed on each variable. The algorithm uses rectangular partitions of the variable domain and a new bounding program based on convex/concave envelopes and positive definite combinations of quadratic terms. The algorithm is deterministic and obtains convergence with final regions of finite size. The partitioning strategy uses a sensitivity analysis of the bounding program to predict the best variable to split and the split location. Two versions of the algorithm are considered, the first using a local NLP algorithm (MINOS) and the second using a sequence of lower bounding programs in the search fo...
Recent Advances in Global Optimization for Process Synthesis, Design and Control: Enclosure of All Solutions
 Computers and Chemical Engineering
, 1999
"... Recent advances in global optimization for process synthesis, design and control are discussed. After a review of the chemical engineering contributions, we focus on the enclosure of all solutions of nonlinear constrained systems of equations. Important theoretical results are presented accompanied ..."
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Cited by 5 (0 self)
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Recent advances in global optimization for process synthesis, design and control are discussed. After a review of the chemical engineering contributions, we focus on the enclosure of all solutions of nonlinear constrained systems of equations. Important theoretical results are presented accompanied with computational studies on the enclosure of multiple steady states and all homogeneous azeotropes. 1 Introduction and Review A significant effort has been expended in the last four decades toward theoretical and algorithmic studies of applications that arise in Chemical Engineering Process Design, Process Synthesis, Process Control, as well as in Computational Chemistry and Molecular Biology. In the last decade we have experienced a dramatic growth of interest in Chemical Engineering for new methods of global optimization and their application to important engineering, as well as computational chemistry and molecular biology problems. Contributions from the chemical engineering communit...
Global Optimization In Design And Control Of Chemical Process Systems
 J. of Proc. Control
, 2001
"... : This paper presents an overview of the recent advances in deterministic global optimization approaches and their applications in the areas of Process Design and Control. The focus is on global optimization methods for (a) twicedifferentiable constrained nonlinear optimization problems, (b) mixed ..."
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Cited by 3 (0 self)
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: This paper presents an overview of the recent advances in deterministic global optimization approaches and their applications in the areas of Process Design and Control. The focus is on global optimization methods for (a) twicedifferentiable constrained nonlinear optimization problems, (b) mixedinteger nonlinear optimization problems, and (c) locating all solutions of nonlinear systems of equations. Theoretical advances and computational studies on process design, batch design under uncertainty, phase equilibrium, location of azeotropes, stability margin, process synthesis, and parameter estimation problems are discussed. Keywords: Global Optimization; Twice Differentiable NLPs; MixedInteger Nonlinear Optimization; Locating All Solutions; ffBB approach, Design and Control 1. INTRODUCTION A significant effort has been expended in the last five decades toward theoretical and algorithmic studies of applications that arise in Process Design and Control. In the last decade we have expe...
Global Optimization Test Problems with Solutions
"... Appendix of problem definitions and solutions for "Branch and Bound for Global NLP: Iterative LP Algorithm & Results" in the monograph "Global Optimization in Engineering Design" [1]. A Detailed Problem Descriptions Filename: fp_2_1.def Description: Chapter 2, Test Problem 1 [2], a concave quadrat ..."
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Cited by 2 (0 self)
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Appendix of problem definitions and solutions for "Branch and Bound for Global NLP: Iterative LP Algorithm & Results" in the monograph "Global Optimization in Engineering Design" [1]. A Detailed Problem Descriptions Filename: fp_2_1.def Description: Chapter 2, Test Problem 1 [2], a concave quadratic program min x 1 (1) s.t. \Gammax 1 + 42x 2 + 44x 3 + 45x 4 + 47x 5 + 47:5x 6 + \Gamma50x 2 x 2 + \Gamma50x 3 x 3 + \Gamma50x 4 x 4 + \Gamma50x 5 x 5 + \Gamma50x 6 x 6 0 20x 2 + 12x 3 + 11x 4 + 7x 5 + 4x 6 40 \Gamma250 x 1 225:5 0 x 2 ; x 3 ; x 4 ; x 5 ; x 6 1 Solution Objective17 x 1 17 x 2 1 x 3 1 x 4 0 x 5 1 x 6 0 Filename: fp_2_2.def Description: Chapter 2, Test Problem 2 (with nonrestrictive variable bounds added) [2], a concave quadratic program min x 1 (2) s.t. \Gammax 1 + \Gamma10:5x 2 + \Gamma7:5x 3 + \Gamma3:5x 4 + \Gamma2:5x 5 + \Gamma1:5x 6 + \Gamma10x 7 + \Gamma0:5x 2 x 2 + \Gamma0:5x 3 x 3 + \Gamma0:5x 4 x 4 + \Gamma0:5x 5 x 5 + \Gamma0:5x 6 x 6 0 6x 2 + 3...
unknown title
, 1996
"... A global MINLP optimization algorithm for the synthesis of heat exchanger networks with no stream splits ..."
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A global MINLP optimization algorithm for the synthesis of heat exchanger networks with no stream splits
Global minimization using an Augmented Lagrangian method with variable lowerlevel constraints
, 2006
"... A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems. At each outer iteration the method requires the εglobal minimization of the Augmented Lagrangian with simple constraints. Global convergence to an ..."
Abstract
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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 the method requires the εglobal minimization of the Augmented Lagrangian with simple constraints. Global convergence to an εglobal minimizer of the original problem is proved. The subproblems are solved using the αBB method. Numerical experiments are presented. Key words: deterministic global optimization, Augmented Lagrangians, nonlinear programming, algorithms, numerical experiments. 1