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Polynomial Optimization

In: Convex Analysis and Global Optimization

Author

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  • Hoang Tuy

    (Institute of Mathematics)

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.

Suggested Citation

  • Hoang Tuy, 2016. "Polynomial Optimization," Springer Optimization and Its Applications, in: Convex Analysis and Global Optimization, edition 2, chapter 0, pages 435-452, Springer.
    • Handle: RePEc:spr:spochp:978-3-319-31484-6_12
    DOI: 10.1007/978-3-319-31484-6_12
    as

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