A uniqueness theorem of supporting hyperplanes for a class of convex level sets in a Hilbert space is obtained. As an application of this result, we prove an alternative theorem on solutions of variational inequalities defined on convex level sets. Three examples are given to demonstrate the...

On the basis of a new topological minimax theorem, a simple and unified approach is developed to Lagrange duality in nonconvex quadratic programming. Diverse generalizations as well as equivalent forms of the S-Lemma, providing a thorough study of duality for single constrained quadratic...

In this work, strong convergence theorems by the viscosity approximation method associated with Meir–Keeler contractions are established for solving fixed point problems of a nonexpansive semigroup, a system of equilibrium problems and variational inequality problems in a real Hilbert space....

This paper is devoted to developing new applications from the limiting subdifferential in nonsmooth optimization and variational analysis to the study of the Lipschitz behavior of the Pareto solution maps in parametric nonconvex semi-infinite vector optimization problems (SIVO for brevity). We...

The majority of Combinatorial Optimization Problems (COPs) are defined in the discrete space. Hence, proposing an efficient algorithm to solve the problems has become an attractive subject in recent years. In this paper, a meta-heuristic algorithm based on Binary Particle Swarm Algorithm (BPSO)...

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...

In previous work, we, and also Epperly and Pistikopoulos, proposed an analysis of general nonlinear programs that identified certain variables as convex, not ever needing subdivision, and non-convex, or possibly needing subdivision in branch and bound algorithms. We proposed a specific...

The Powell singular function was introduced 1962 by M.J.D. Powell as an unconstrained optimization problem. The function is also used as nonlinear least squares problem and system of nonlinear equations. The function is a classic test function included in collections of test problems in...

We propose higher-order radial sets and corresponding derivatives of a set-valued map and prove calculus rules for sums and compositions, which are followed by direct applications in discussing optimality conditions for several particular optimization problems. Our main results are both...

In this paper, we first obtain some properties of topical (increasing and plus-homogeneous) functions in the framework of abstract convexity. Next, we use the Toland–Singer formula to characterize the dual problem for the difference of two topical functions. Finally, we present necessary and...