Moment approximations for set-semidefinite polynomials
Dickinson, Peter J. C. (Author), Povh, Janez (Author)

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The set of polynomials that are nonnegative over a subset of the nonnegative orthant (we call them set-semidefinite) have many uses in optimization. A common example of this type set is the set of copositive matrices, where we are effectively considering nonnegativity over the entire nonnegative orthant and are restricted to homogeneous polynomials of degree two. Lasserre (SIAM J. Optim., 21(3):864885, 2011) has previously considered a method using moments in order to provide an outer approximation to this set, for nonnegativity over a general subset of the real space. In this paper, we shall show that, in the special case of considering nonnegativity over a subset of the nonnegative orthant, we can provide a new outer approximation hierarchy. This is based on restricting moment matrices to be completely positive, and it is at least as good as Lasserres method. This can then be relaxed to give tractable approximations that are still at least as good as Lasserres method. In doing this, we also provide interesting new insights into the use of moments in constructing these approximations.

Keywords:nonnegative polynomials, set-semidefinite polynomials, copositive programming, Doubly nonnegative matrices, Moments, Completely positive matrices
Work type:Not categorized (r6)
Tipology:1.01 - Original Scientific Article
Organization:NTF - Faculty of Natural Sciences and Engineering
Number of pages:str. 57-68
Numbering:Vol. 159, issue 1
ISSN on article:1573-2878
DOI:10.1007/s10957-013-0279-7 Link is opened in a new window
COBISS.SI-ID:2048193299 Link is opened in a new window
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Record is a part of a journal

Title:Journal of optimization theory and applications
Shortened title:J. optim. theory appl.
COBISS.SI-ID:513199641 This link opens in a new window

Secondary language

Keywords:nenegativni polinomi, pogojno pozitivni polinomi, kopozitivno programiranje, dvojno nenegativne matrike, momenti, popolnoma pozitivne matrike

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