Farkas’ lemma: three decades of generalizations for mathematical optimization

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

(2013) V. Jeyakumar et al.   APPLICABLE ANALYSIS

Functional inequalities and theorems of the alternative involving composite functions

(2013) N. Dinh et al.   JOURNAL OF GLOBAL OPTIMIZATION

Dual Semidefinite Programs Without Duality Gaps for a Class of Convex Minimax Programs

(2013) V. Jeyakumar et al.   JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

Robust linear semi-infinite programming duality under uncertainty

(2013) M. A. Goberna et al.   MATHEMATICAL PROGRAMMING

An approximate Hahn–Banach theorem for positively homogeneous functions

(2013) N. Dinh et al.   OPTIMIZATION

Farkas-type theorems for positively homogeneous systems in ordered topological vector spaces

(2012) A.R. Doagooei   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

A convex polynomial that is not sos-convex

(2011) Amir Ali Ahmadi et al.   MATHEMATICAL PROGRAMMING

Duality and Farkas-type results for extended Ky Fan inequalities with DC functions

(2011) X. K. Sun et al.   Optimization Letters

Theory and Applications of Robust Optimization

(2011) Dimitris Bertsimas et al.   SIAM REVIEW

Duality and Farkas-type results for DC fractional programming with DC constraints

(2010) Hai-Jun Wang et al.   MATHEMATICAL AND COMPUTER MODELLING

Characterizing robust set containments and solutions of uncertain linear programs without qualifications

(2010) V. Jeyakumar et al.   OPERATIONS RESEARCH LETTERS

Robust Farkas’ lemma for uncertain linear systems with applications

(2010) V. Jeyakumar et al.   POSITIVITY

Convex Inequalities Without Constraint Qualification nor Closedness Condition, and Their Applications in Optimization

(2010) N. Dinh et al.   Set-Valued and Variational Analysis

Strong Duality in Robust Convex Programming: Complete Characterizations

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

On the Stability of the Feasible Set in Optimization Problems

(2010) N. Dinh et al.   SIAM JOURNAL ON OPTIMIZATION

Functional Inequalities in the Absence of Convexity and Lower Semicontinuity with Applications to Optimization

(2010) N. Dinh et al.   SIAM JOURNAL ON OPTIMIZATION

Duality and optimality conditions for generalized equilibrium problems involving DC functions

(2009) N. Dinh et al.   JOURNAL OF GLOBAL OPTIMIZATION

Subdifferentials of value functions and optimality conditions for DC and bilevel infinite and semi-infinite programs

(2009) N. Dinh et al.   MATHEMATICAL PROGRAMMING

Farkas’ lemma for separable sublinear inequalities without qualifications

(2009) V. Jeyakumar et al.   Optimization Letters

Alternative Theorems for Quadratic Inequality Systems and Global Quadratic Optimization

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

Stable and Total Fenchel Duality for Convex Optimization Problems in Locally Convex Spaces

(2009) Chong Li et al.   SIAM JOURNAL ON OPTIMIZATION

Constraint Qualifications for Extended Farkas's Lemmas and Lagrangian Dualities in Convex Infinite Programming

(2009) D. H. Fang et al.   SIAM JOURNAL ON OPTIMIZATION

Semidefinite representation of convex sets

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

A closedness condition and its applications to DC programs with convex constraints

(2008) N. Dinh et al.   OPTIMIZATION

Necessary and sufficient constraint qualifications for solvability of systems of infinite convex inequalities

(2006) M.A. Goberna et al.   NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS