The complexity of optimizing over a simplex, hypercube or sphere: a short survey (English)

In: Central European Journal of Operations Research   ;  16 ,  2  ;  111-125  ;  2007

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Abstract We consider the computational complexity of optimizing various classes of continuous functions over a simplex, hypercube or sphere. These relatively simple optimization problems arise naturally from diverse applications. We review known approximation results as well as negative (inapproximability) results from the recent literature.

Table of contents – Volume 16, Issue 2

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107
Editorial
Stein, Oliver / Still, Georg / Terlaky, Tamás / Weber, Gerhard-Wilhelm | 2008
111
The complexity of optimizing over a simplex, hypercube or sphere: a short survey
Klerk, Etienne | 2007
127
LaGO: a (heuristic) Branch and Cut algorithm for nonconvex MINLPs
Nowak, Ivo / Vigerske, Stefan | 2007
139
A computational comparison of some branch and bound methods for indefinite quadratic programs
Cambini, Riccardo / Sodini, Claudio | 2007
153
A sequential method for a class of pseudoconcave fractional problems
Carosi, Laura / Martein, Laura | 2007
165
Model development and optimization in interactive computing environments
Pintér, János D. | 2008
179
Cascading: an adjusted exchange method for robust conic programming
Werner, Ralf | 2007
191
The financial equilibrium problem with implicit budget constraints
Scrimali, Laura | 2007
205
Uniform LP duality for semidefinite and semi-infinite programming
Zhang, Qinghong | 2007
215
Bi-parametric optimal partition invariancy sensitivity analysis in linear optimization
Ghaffari-Hadigheh, Alireza / Ghaffari-Hadigheh, Habib / Terlaky, Tamás | 2008