A new class of alternative theorems for SOS-convex inequalities and robust optimization

A Complete Characterization of the Gap between Convexity and SOS-Convexity

(2013) Amir Ali Ahmadi et al.   SIAM JOURNAL ON OPTIMIZATION

Constraint qualifications in linear vector semi-infinite optimization

(2012) M.A. Goberna et al.   EUROPEAN JOURNAL OF OPERATIONAL RESEARCH

Exact SDP relaxations for classes of nonlinear semidefinite programming problems

(2012) V. Jeyakumar et al.   OPERATIONS RESEARCH LETTERS

A convex polynomial that is not sos-convex

(2011) Amir Ali Ahmadi et al.   MATHEMATICAL PROGRAMMING

A robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty

(2011) V. Jeyakumar et al.   OPERATIONS RESEARCH LETTERS

Strong Duality in Robust Convex Programming: Complete Characterizations

(2010) V. Jeyakumar et al.   SIAM JOURNAL ON OPTIMIZATION

Necessary global optimality conditions for nonlinear programming problems with polynomial constraints

(2009) V. Jeyakumar et al.   MATHEMATICAL PROGRAMMING

Alternative Theorems for Quadratic Inequality Systems and Global Quadratic Optimization

(2009) V. Jeyakumar et al.   SIAM JOURNAL ON OPTIMIZATION

Semidefinite representation of convex sets

(2008) J. William Helton et al.   MATHEMATICAL PROGRAMMING

Duality in robust optimization: Primal worst equals dual best

(2008) Amir Beck et al.   OPERATIONS RESEARCH LETTERS

Necessary and sufficient conditions for S-lemma and nonconvex quadratic optimization

(2008) Vaithilingam Jeyakumar et al.   OPTIMIZATION AND ENGINEERING