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We consider real polynomials in finitely many variables. Let the variables consist of finitely many blocks that are allowed to overlap in a certain way. Let the solution set of a finite system of polynomial inequalities be given where each inequality involves only variables of one block. We investigate polynomials that are positive on such a set and sparse(More)
We show that every real polynomial f nonnegative on [−1, 1] n can be approximated in the l 1-norm of coefficients, by a sequence of polynomials {f εr } that are sums of squares. This complements the existence of s.o.s. approximations in the denseness result of Berg, Christensen and Ressel, as we provide a very simple and explicit approximation sequence.(More)
This work is concerned with different aspects of spectrahedra and their projections, sets that are important in semidefinite optimization. We prove results on the limitations of so called Lasserre and theta body relaxation methods for semialgebraic sets and varieties. As a special case we obtain the main result of [19] on non-exposed faces. We also solve(More)
A finitely generated quadratic module or preordering in the real polynomial ring is called stable, if it admits a certain degree bound on the sums of squares in the representation of polynomials. Stability, first defined explicitly in [PS], is a very useful property. It often implies that the quadratic module is closed; furthermore it helps settling the(More)
This paper explores a general model of the evolution and adaption of hedonic utility. It is shown that optimal utility will be increasing strongly in regions where choices have to be made often and decision mistakes have a severe impact on fitness. Several applications are suggested. In the context of intertemporal preferences, the model offers an(More)
Gewidmet meinen Eltern Marina und Michael Plaumann und meinem Onkel Peter Plaumann in tiefer Dankbarkeit Acknowledgements I would like to express my gratitude to my advisor Claus Scheiderer for the many ideas and insights into the topic that he shared with me, as well as for his constant encouragement. I am grateful for many interesting and helpful(More)
A linear matrix inequality (LMI) is a condition stating that a symmetric matrix whose entries are affine-linear combinations of variable,; is positive semidefinite. :dotiv11ted by the fact that diagonal LMIs define polyhedra, the solution set of an LMI is called a spectrahedron. Linear images of spectrahedra are called semidefinitely representable sets.(More)
We consider the problem of determining the closure M of a quadratic module M in a commutative R-algebra with respect to the finest locally convex topology. This is of interest in deciding when the moment problem is solvable [26] [27] and in analyzing algorithms for polynomial optimization involving semi-definite programming [12]. The closure of a(More)