DC decomposition of nonconvex polynomials with algebraic techniques

DOI10.1007/s10107-017-1144-5zbMath1390.90418arXiv1510.01518OpenAlexW2963840269MaRDI QIDQ1749445

Georgina Hall, Amir Ali Ahmadi

Publication date: 16 May 2018

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.01518

zbMATH Keywords

polynomial optimizationdifference of convex programmingalgebraic decomposition of polynomialsconic relaxations

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Semidefinite programming (90C22) Abstract computational complexity for mathematical programming problems (90C60) Nonconvex programming, global optimization (90C26)

Related Items (6)

A linear programming approach to difference-of-convex piecewise linear approximation ⋮ Block-sparse recovery of semidefinite systems and generalized null space conditions ⋮ On the complexity of testing attainment of the optimal value in nonlinear optimization ⋮ Estimation from nonlinear observations via convex programming with application to bilinear regression ⋮ D.C. programming for sparse proximal support vector machines ⋮ Encoding inductive invariants as barrier certificates: synthesis via difference-of-convex programming

Uses Software

• Mosek
• SPOTless

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A convex polynomial that is not sos-convex
• On functions representable as a difference of convex functions
• Semidefinite representation of convex sets
• Convergence and restart in branch-and-bound algorithms for global optimization. Application to concave minimization and d.c. optimization problems
• Reverse convex programming
• Solving a class of linearly constrained indefinite quadratic problems by DC algorithms
• Convex analysis approach to d. c. programming: Theory, algorithms and applications
• A parametric characterization of local optimality
• Second-order cone programming
• Semidefinite programming relaxations for semialgebraic problems
• Undominated d.c. decompositions of quadratic functions and applications to branch-and-bound approaches
• NP-hardness of deciding convexity of quartic polynomials and related problems
• DC programming: overview.
• Variations and extension of the convex-concave procedure
• A DC programming approach for feature selection in support vector machines learning
• How to Integrate a Polynomial over a Sphere
• A Complete Characterization of the Gap between Convexity and SOS-Convexity
• On the Lasserre Hierarchy of Semidefinite Programming Relaxations of Convex Polynomial Optimization Problems
• Robust investment strategies with discrete asset choice constraints using DC programming
• Biquadratic Optimization Over Unit Spheres and Semidefinite Programming Relaxations
• Convexity in SemiAlgebraic Geometry and Polynomial Optimization
• Global minimization of a difference of two convex functions
• A New Decomposition Method for Multiuser DC-Programming and Its Applications
• Computational Aspects of Constrained L 1-L 2 Minimization for Compressive Sensing
• DSOS and SDSOS Optimization: More Tractable Alternatives to Sum of Squares and Semidefinite Optimization
• 10.1162/153244303765208403

This page was built for publication: DC decomposition of nonconvex polynomials with algebraic techniques