Journal
COMPUTERS & CHEMICAL ENGINEERING
Volume 29, Issue 6, Pages 1185-1202Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.compchemeng.2005.02.006
Keywords
global optimization; nonlinear optimization; mixed-integer nonlinear optimization; differential-algebraic optimization; optimization with nonfactorable/grey-box models; bilevel nonlinear optimization; nonconvexities; convex envelopes; convex underestimators; trilinear monomials; trigonometric functions; twice continuously differentiable functions
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This paper presents an overview of the research progress in global optimization during the last 5 years (1998-2003), and a brief account of our recent research contributions. The review part covers the areas of (a) twice continuously differentiable nonlinear optimization, (b) mixed-integer nonlinear optimization, (c) optimization with differential-algebraic models, (d) optimization with grey-box/black-box/nonfactorable models, and (e) bilevel nonlinear optimization. Our research contributions part focuses on (i) improved convex underestimation approaches that include convex envelope results for multilinear functions, convex relaxation results for trigonometric functions, and a piecewise quadratic convex underestimator for twice continuously differentiable functions, and (ii) the recently proposed novel generalized alpha BB framework. Computational studies will illustrate the potential of these advances. (c) 2005 Elsevier Ltd. All rights reserved.
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