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Polynomial Optimization

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Convex Analysis and Global Optimization

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 110))

Abstract

Polynomial optimization is concerned with optimization problems described by multivariate polynomials on \(\mathbb{R}_{+}^{n}.\) In this chapter two approaches are presented for polynomial optimization. In the first approach a polynomial optimization problem is solved as a nonconvex optimization problem by a rectangular branch and bound algorithm in which bounding is performed by linear or convex relaxation. In the second approach, by viewing any multivariate polynomial on \(\mathbb{R}_{+}^{n}\) as a difference of two increasing functions, a polynomial optimization problem is treated as a monotonic optimization problem. In particular, the Successive Incumbent Transcending algorithm is developed which starts from a quickly found feasible solution then proceeds to gradually improving it to optimality.

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Tuy, H. (2016). Polynomial Optimization. In: Convex Analysis and Global Optimization. Springer Optimization and Its Applications, vol 110. Springer, Cham. https://doi.org/10.1007/978-3-319-31484-6_12

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