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- W2950002149 abstract "Consider the optimization problem $p_{min, Q} := min_{mathbf{x} in Q} p(mathbf{x})$, where $p$ is a degree $m$ multivariate polynomial and $Q := [0, 1]^n$ is the hypercube. We provide explicit degree and error bounds for the sums of squares approximations of $p_{min, Q}$ corresponding to the Positivstellensatz of Putinar. Our approach uses Bernstein multivariate approximation of polynomials, following the methodology of De Klerk and Laurent to provide error bounds for Schmudgen type positivity certificates over the hypercube. We give new bounds for Putinar type representations by relating the quadratic module and the preordering associated with the polynomials $g_i := x_i (1 - x_i), : i=1,dots,n$, describing the hypercube $Q$." @default.
- W2950002149 created "2019-06-27" @default.
- W2950002149 creator A5066095974 @default.
- W2950002149 date "2014-04-24" @default.
- W2950002149 modified "2023-09-25" @default.
- W2950002149 title "Error Bounds for Polynomial Optimization over the Hypercube using Putinar type Representations" @default.
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