Global optimization in the 21st century: Advances and challenges

• Published in: Computers & chemical engineering Vol. 29; no. 6; pp. 1185 - 1202
• Main Authors: Floudas, C.A., Akrotirianakis, I.G., Caratzoulas, S., Meyer, C.A., Kallrath, J.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 15.05.2005
• Subjects: Bilevel nonlinear optimization; Convex envelopes; Convex underestimators; Differential-algebraic optimization; Global optimization; Mixed-integer nonlinear optimization; Nonconvexities; Nonlinear optimization; Optimization with nonfactorable/grey-box models; Trigonometric functions; Trilinear monomials; Twice continuously differentiable functions; Global optimization; Differential-algebraic optimization; Twice continuously differentiable functions; Bilevel nonlinear optimization; Convex envelopes; Optimization with nonfactorable/grey-box models; Nonconvexities; Nonlinear optimization; Convex underestimators; Trigonometric functions; Trilinear monomials; Mixed-integer nonlinear optimization
• ISSN: 0098-1354; 1873-4375
• DOI: 10.1016/j.compchemeng.2005.02.006

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 α BB framework. Computational studies will illustrate the potential of these advances.