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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.
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...
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...
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