We consider the following generalized vector optimization problem (GVOP): (2.3).
The generalized vector optimization problem : finding such that.
Algorithmically, the Grothendieck constant can be viewed as the integrality gap between what can be attained by a general (vector) solution and the integral solution to the optimization problem of maximizing.
Rong and Wu [3] considered cone-subconvexlike vector optimization problems with set-valued maps in general spaces and derived scalarization results, ϵ-saddle point theorems, and ϵ-duality assertions using ϵ-Lagrangian multipliers.
On the other hand, the vector equilibrium problem provides a very general model for a wide range of problems, for example, the vector optimization problem, the vector variational inequality problem, the vector complementarity problem and the vector saddle point problem.
It provides a very general model for a wide range of problems, for example, the vector optimization problem, the vector variational inequality problem, the vector complementarity problem and the vector saddle point problem.
It is well-known that VEP provides a general model of several classes of problems such as the vector variational inequality, the vector complementarity problems, the vector optimization problems, the vector saddle point (minimax) problems, the multiobjective game problems, and fixed point problems (see, e.g., [2 9] and the references therein).
It is well known that the vector equilibrium problem (VEP, in short) is a very general mathematical model, which embraces the formats of several disciplines, as those for Nash equilibria, those from Game Theory, those from (Vector) Optimization and (Vector) Variational Inequalities, and so on (see [1 4]).
simple general vector n. a simple vector.
Scalar versus vector optimization problems from systems engineering and architecting of complex systems.
