Please use this identifier to cite or link to this item:
http://hdl.handle.net/10397/16215
Title: | Standard bi-quadratic optimization problems and unconstrained polynomial reformulations | Authors: | Bomze, IM Ling, C Qi, L Zhang, X |
Keywords: | Bi-quartic optimization Optimality conditions Penalty function Polynomial optimization Standard simplex |
Issue Date: | 2012 | Publisher: | Springer | Source: | Journal of global optimization, 2012, v. 52, no. 4, p. 663-687 How to cite? | Journal: | Journal of global optimization | Abstract: | A so-called Standard Bi-Quadratic Optimization Problem (StBQP) consists in minimizing a bi-quadratic form over the Cartesian product of two simplices (so this is different from a Bi-Standard QP where a quadratic function is minimized over the same set). An application example arises in portfolio selection. In this paper we present a bi-quartic formulation of StBQP, in order to get rid of the sign constraints. We study the first- and second-order optimality conditions of the original StBQP and the reformulated bi-quartic problem over the product of two Euclidean spheres. Furthermore, we discuss the one-to-one correspondence between the global/local solutions of StBQP and the global/local solutions of the reformulation. We introduce a continuously differentiable penalty function. Based upon this, the original problem is converted into the problem of locating an unconstrained global minimizer of a (specially structured) polynomial of degree eight. | URI: | http://hdl.handle.net/10397/16215 | ISSN: | 0925-5001 | EISSN: | 1573-2916 | DOI: | 10.1007/s10898-011-9710-5 |
Appears in Collections: | Journal/Magazine Article |
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