Positive polynomials on projective limits of real algebraic varieties |
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Authors: | Salma Kuhlmann Mihai Putinar |
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Institution: | a Department of Mathematics and Statistics, University of Saskatchewan, S7N 5E6, Canada b Mathematics Department, University of California, Santa Barbara, CA 93106, USA |
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Abstract: | We reveal some important geometric aspects related to non-convex optimization of sparse polynomials. The main result, a Positivstellensatz on the fibre product of real algebraic affine varieties, is iterated to a comprehensive class of projective limits of such varieties. This framework includes as necessary ingredients recent works on the multivariate moment problem, disintegration and projective limits of probability measures and basic techniques of the theory of locally convex vector spaces. A variety of applications illustrate the versatility of this novel geometric approach to polynomial optimization. |
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Keywords: | Positive polynomial Non-convex optimization Moment problem Fibre product Projective limit |
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