Solving polynomial optimization problems via the truncated tangency variety and sums of squares

DOI10.1016/j.jpaa.2009.03.014zbMath1163.14314OpenAlexW2070850517MaRDI QIDQ1030710

Tiên Sȯn Phạm, Ha Huy Vui

Publication date: 2 July 2009

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2009.03.014

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Semialgebraic sets and related spaces (14P10)

Related Items (16)

Stability and genericity for semi-algebraic compact programs ⋮ Generalized S-lemma and strong duality in nonconvex quadratic programming ⋮ Convergence of the Lasserre hierarchy of SDP relaxations for convex polynomial programs without compactness ⋮ Tangencies and polynomial optimization ⋮ Homogenization for polynomial optimization with unbounded sets ⋮ Equality-constrained minimization of polynomial functions ⋮ Global optimization of polynomials restricted to a smooth variety using sums of squares ⋮ Generic Properties for Semialgebraic Programs ⋮ A Frank-Wolfe type theorem for nondegenerate polynomial programs ⋮ Global optimization of polynomials over real algebraic sets ⋮ Proving inequalities and solving global optimization problems via simplified CAD projection ⋮ Intrinsic complexity estimates in polynomial optimization ⋮ Well-Posedness in Unconstrained Polynomial Optimization Problems ⋮ Solving the equality-constrained minimization problem of polynomial functions ⋮ Minimizing rational functions by exact Jacobian SDP relaxation applicable to finite singularities ⋮ The Łojasiewicz exponent of a continuous subanalytic function at an isolated zero

Uses Software

• Sostools

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Representations of positive polynomials on noncompact semialgebraic sets via KKT ideals
• Semidefinite representations for finite varieties
• Bifurcation sets of functions definable in \(o\)-minimal structures
• The \(K\)-moment problem for compact semi-algebraic sets
• Milnor fibration at infinity
• Tame geometry with application in smooth analysis
• Geometry of real polynomial mappings
• Minimizing polynomials via sum of squares over the gradient ideal
• Global Optimization with Polynomials and the Problem of Moments
• Global Optimization of Polynomials Using the Truncated Tangency Variety and Sums of Squares
• An approach to obtaining global extremums in polynomial mathematical programming problems
• Numerical Optimization
• Optimization of Polynomial Functions
• Optimization of Polynomials on Compact Semialgebraic Sets
• Singular Points of Complex Hypersurfaces. (AM-61)
• Global Optimization of Polynomials Using Gradient Tentacles and Sums of Squares

This page was built for publication: Solving polynomial optimization problems via the truncated tangency variety and sums of squares