Global optimality conditions and optimization methods for quadratic assignment problems

Global Optimality Conditions for Quadratic Optimization Problems with Binary Constraints

We consider nonconvex quadratic optimization problems with binary constraints. Our main result identifies a class of quadratic problems for which a given feasible point is global optimal. We also establish a necessary global optimality condition. These conditions are expressed in a simple way in terms of the problem’s data. We also study the relations between optimal solutions of the nonconvex ...

Global Optimality Conditions for Optimization Problems∗

We establish new necessary and sufficient optimality conditions for optimization problems. In particular, we establish tractable optimality conditions for the problems of minimizing a weakly convex or concave function subject to standard constraints, such as box constraints, binary constraints, and simplex constraints. Our main theoretical tool for establishing these optimality conditions is ab...

Global and local optimality conditions in set-valued optimization problems

Through the paper, X and Y are normed vector spaces; however, most of the results remain true in the more general setting of locally convex spaces. We denote by X∗ and Y∗ the topological dual spaces of X and Y . We consider a pointed closed convex cone Q ⊂ Y which introduces a partial order on Y by the equivalence y1 ≤Q y2 ⇔ y2 − y1 ∈Q; we also suppose, in general, that Q has nonempty interior....

Chaotic optimization for quadratic assignment problems

Sufficient global optimality conditions for general mixed integer nonlinear programming problems

‎In this paper‎, ‎some KKT type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (MINPP) are established‎. ‎We achieve‎ ‎this by employing a Lagrange function for MINPP‎. ‎In addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...