Polynomial Optimization

Hoang Tuy
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Hoang Tuy: Institute of Mathematics

Chapter Chapter 12 in Convex Analysis and Global Optimization, 2016, pp 435-452 from Springer

Abstract: Abstract Polynomial optimization is concerned with optimization problems described by multivariate polynomials on ℝ + n . $$\mathbb{R}_{+}^{n}.$$ 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 ℝ + n $$\mathbb{R}_{+}^{n}$$ 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.

Keywords: Polynomial Optimization Problems; Monotonic Optimization; Signomial Programming; Master Problem; Reformulation-Linearization Technique (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-31484-6_12

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