When is a point x satisfying $\nabla f(x)= 0 a global minimum of f?
American Mathematical Monthly
Convex programs with an additional reverse convex constraint
Journal of Optimization Theory and Applications
A level set algorithm for a class for reverse convex programs
Annals of Operations Research
A new cutting plane-algorithm for a class of reverse convex 0–1 integer programs
Recent advances in global optimization
Implicit enumeration for the pure integer 0/1 minimax programming problem
Operations Research
A Convex Envelope Formula for Multilinear Functions
Journal of Global Optimization
Testing the Re- strategy for a Reverse Convex Problem
Journal of Global Optimization
Conditions for Global Optimality 2
Journal of Global Optimization
Remarks on an algorithm for reverse convex programs
Journal of Global Optimization
Subset Algebra Lift Operators for 0-1 Integer Programming
SIAM Journal on Optimization
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Outer approximation algorithms for canonical DC problems
Journal of Global Optimization
Approximate optimality conditions and stopping criteria in canonical DC programming
Optimization Methods & Software - DEDICATED TO PROFESSOR VLADIMIR F. DEMYANOV ON THE OCCASION OF HIS 70TH BIRTHDAY
Canonical DC programming problem: Outer approximation methods revisited
Operations Research Letters
On the convergence of the block nonlinear Gauss-Seidel method under convex constraints
Operations Research Letters
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The paper proposes a new necessary and sufficient global optimality condition for canonical DC optimization problems. We analyze the rationale behind Tuy's standard global optimality condition for canonical DC problems, which relies on the so-called regularity condition and thus can not deal with the widely existing non-regular instances. Then we show how to modify and generalize the standard condition to a new one that does not need regularity assumption, and prove that this new condition is equivalent to other known global optimality conditions. Finally, we show that the cutting plane method, when associated with the new optimality condition, could solve the non-regular canonical DC problems, which significantly enlarges the application of existing cutting plane (outer approximation) algorithms.