On minimizing difference of a SOS-convex polynomial and a support function over a SOS-concave matrix polynomial constraint
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Publication:1749450
DOI10.1007/s10107-017-1210-zzbMath1390.90518OpenAlexW2769757009MaRDI QIDQ1749450
Publication date: 16 May 2018
Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10107-017-1210-z
strong dualityDC programmingsums of squares polynomialsset containmentSOS-convex polynomialsSOS-concave matrix
Semidefinite programming (90C22) Nonlinear programming (90C30) Convexity of real functions in one variable, generalizations (26A51)
Related Items (3)
Conic relaxations with stable exactness conditions for parametric robust convex polynomial problems ⋮ Sum-of-squares relaxations in robust DC optimization and feature selection ⋮ On semidefinite programming relaxations for a class of robust SOS-convex polynomial optimization problems
Uses Software
Cites Work
- Generalized Farkas' lemma and gap-free duality for minimax DC optimization with polynomials and robust quadratic optimization
- Semidefinite programming relaxation methods for global optimization problems with sparse polynomials and unbounded semialgebraic feasible sets
- Dual semidefinite programs without duality gaps for a class of convex minimax programs
- Trust-region problems with linear inequality constraints: exact SDP relaxation, global optimality and robust optimization
- Lagrange-type duality in DC programming
- A convex polynomial that is not sos-convex
- Duality for multiobjective optimization problems with convex objective functions and D.C. constraints
- Semidefinite representation of convex sets
- Subdifferentials of value functions and optimality conditions for DC and bilevel infinite and semi-infinite programs
- Some new Farkas-type results for inequality systems with DC functions
- Characterizing robust set containments and solutions of uncertain linear programs without qualifications
- Concave duality: Application to problems dealing with difference of functions
- Extremal psd forms with few terms
- Duality in nonconvex optimization
- A general duality scheme for nonconvex minimization problems with a strict inequality constraint
- Duality in D. C. programming: The case of several D. C. constraints
- Solving a class of linearly constrained indefinite quadratic problems by DC algorithms
- A Frank--Wolfe type theorem for convex polynomial programs
- The DC (Difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems
- Sparsity in sums of squares of polynomials
- Sequential Lagrangian conditions for convex programs with applications to semidefinite programming
- Exact SDP relaxations for classes of nonlinear semidefinite programming problems
- Robust SOS-convex polynomial optimization problems: exact SDP relaxations
- Lagrange duality in canonical DC programming
- Dual characterizations of set containments with strict convex inequalities
- A Complete Characterization of the Gap between Convexity and SOS-Convexity
- Polynomial Matrix Inequality and Semidefinite Representation
- Stable and Total Fenchel Duality for DC Optimization Problems in Locally Convex Spaces
- DC Programming and DCA for General DC Programs
- DC Programming Approaches for BMI and QMI Feasibility Problems
- Convexity in SemiAlgebraic Geometry and Polynomial Optimization
- Duality in Reverse Convex Optimization
- Characterizing Set Containments Involving Infinite Convex Constraints and Reverse-Convex Constraints
- New Sequential Lagrange Multiplier Conditions Characterizing Optimality without Constraint Qualification for Convex Programs
- Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
- A new class of alternative theorems for SOS-convex inequalities and robust optimization
- Solving the Quadratic Eigenvalue Complementarity Problem by DC Programming
- Sums of Squares and Semidefinite Program Relaxations for Polynomial Optimization Problems with Structured Sparsity
- Convex Analysis
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