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Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models.Often, it is known beforehand, that the underlying unknown function has certain properties, e.g. nonnegative or increasing on a certain region.However,...
Persistent link: https://www.econbiz.de/10011090673
AMS classifications: 65D05; 65K05; 90C22;
Persistent link: https://www.econbiz.de/10011091008
We review complexity results for minimizing polynomials over the standard simplex and unit hypercube.In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing Lipschitz continuous functions and functions with uniformly bounded Hessians over the standard...
Persistent link: https://www.econbiz.de/10011091363
We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower bounds for several instances of quadratic assignment problems from the problem library: [R.E....
Persistent link: https://www.econbiz.de/10011090357
AMS classification: 90C22, 20Cxx, 70-08
Persistent link: https://www.econbiz.de/10011090442
AMS classification: 90C22, 20Cxx, 70-08
Persistent link: https://www.econbiz.de/10011090924
AMS classification: 90C22, 20Cxx, 70-08
Persistent link: https://www.econbiz.de/10011090982
In this paper we present the algorithmic framework and practical aspects of implementing a parallel version of a primal-dual semidefinite programming solver on a distributed memory computer cluster. Our implementation is based on the CSDP solver and uses a message passing interface (MPI), and...
Persistent link: https://www.econbiz.de/10011091373
AMS classification: 90C22, 20Cxx, 70-08
Persistent link: https://www.econbiz.de/10011091737
The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO).It is NPhard, and contains the maximum stable set problem in graphs as a special case.In this note we show that the SQO problem may be reformulated as an...
Persistent link: https://www.econbiz.de/10011092227