A review of recent advances in global optimization

This paper presents an overview of the research progress in deterministic global optimization during the last decade (1998–2008). It covers the areas of twice continuously differentiable nonlinear optimization, mixed-integer nonlinear optimization, optimization with differential-algebraic models, semi-infinite programming, optimization with grey box/nonfactorable models, and bilevel nonlinear optimization.

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[66]  Nikolaos V. Sahinidis,et al.  Analysis of Bounds for Multilinear Functions , 2001, J. Glob. Optim..

[67]  Nikolaos V. Sahinidis,et al.  Global Optimization of 0-1 Hyperbolic Programs , 2002, J. Glob. Optim..

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[74]  P. I. Barton,et al.  Global Mixed-Integer Dynamic Optimization , 2005 .

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[76]  Paul I. Barton,et al.  Design of process operations using hybrid dynamic optimization , 2004, Comput. Chem. Eng..

[77]  Jung-Fa Tsai,et al.  Finding all solutions of systems of nonlinear equations with free variables , 2007 .

[78]  H. P. Benson,et al.  Solving Sum of Ratios Fractional Programs via Concave Minimization , 2007 .

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[80]  Julio R. Banga,et al.  Global Optimization of Bioprocesses using Stochastic and Hybrid Methods , 2004 .

[81]  Xu Zhihong,et al.  Lipschitz optimization for phase stability analysis: application to Soave–Redlich–Kwong equation of state , 1999 .

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[83]  Zhi-You Wu,et al.  Hidden Convex Minimization , 2005, J. Glob. Optim..

[84]  C. Floudas.  Handbook of Test Problems in Local and Global Optimization , 1999 .

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[86]  Nikolaos V. Sahinidis,et al.  Optimization of metabolic pathways under stability considerations , 2005, Comput. Chem. Eng..

[87]  David Yang Gao,et al.  Canonical Duality Theory and Solutions to Constrained Nonconvex Quadratic Programming , 2004, J. Glob. Optim..

[88]  Ioannis Papamichail,et al.  Proof of Convergence for a Global Optimization Algorithm for Problems with Ordinary Differential Equations , 2005, J. Glob. Optim..

[89]  F. Tardella.  On the existence of polyhedral convex envelopes , 2004 .

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[94]  Ignacio E. Grossmann,et al.  Generalized Convex Disjunctive Programming: Nonlinear Convex Hull Relaxation , 2003, Comput. Optim. Appl..

[95]  Christodoulos A. Floudas,et al.  A New Class of Improved Convex Underestimators for Twice Continuously Differentiable Constrained NLPs , 2004, J. Glob. Optim..

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