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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 9 (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 ..."
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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...
Global minimization using an Augmented Lagrangian method
, 2007
"... with variable lowerlevel constraints ..."
Approved by: PRODUCTIVITY ENHANCEMENT THROUGH PROCESS INTEGRATION
, 2005
"... A hierarchical procedure is developed to determine maximum overall yield of a process and optimize process changes to achieve such a yield. First, a targeting procedure is developed to identify an upper bound of the overall yield ahead of detailed design. Several mass integration strategies are prop ..."
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A hierarchical procedure is developed to determine maximum overall yield of a process and optimize process changes to achieve such a yield. First, a targeting procedure is developed to identify an upper bound of the overall yield ahead of detailed design. Several mass integration strategies are proposed to attain maximum yield. These strategies include rerouting of raw materials, optimization of reaction yield, rerouting of product from undesirable outlets to desirable outlets, and recycling of unreacted raw materials. Path equations are tailored to provide the appropriate level of detail for modeling process performance as a function of the optimization variables pertaining to design and operating variables. Interval analysis is used as an inclusion technique that provides rigorous bounds regardless of the process nonlinearities and without enumeration. Then, a new approach for identification of costeffective implementation of maximum attainable targets for yield is presented. In this approach, a mathematical program was developed to identify the maximum feasible yield using a combination of iterative additions of constraints and problem reformulation. Next, cost objectives were employed to identify a costeffective solution with the details of design and operating
Process Engineering: Part II  A Systems View
"... We discuss the impact over the past forty years of process systems thinking on the design and operation of chemical processes. We first explore the rich set of issues related to design, only part of which are technical. We then examine simulation, optimization and synthesis ideas as they relate to d ..."
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We discuss the impact over the past forty years of process systems thinking on the design and operation of chemical processes. We first explore the rich set of issues related to design, only part of which are technical. We then examine simulation, optimization and synthesis ideas as they relate to design. Finally, we discuss briefly what we see to be the significant issues in plant operation. 2 Introduction Part I of this paper [Krambeck, 1998] looked at the significant role that the concepts of the unit operation and the unit process have had over the past 75 years in chemical process engineering design and operation. Since the mid1960s, we have witnessed a rapidly increasing impact of systems engineering concepts on process engineering design and operation that are largely coincident with the improvements in computing. We seek here in Part II to examine this impact, one that comes from the connecting together of wellunderstood parts to form a larger system. Part III [Keller, 1998...