In this article, we view the Pareto and weak solutions of multiobjective optimization by using an approximate version KKT type conditions. one our main results Ekeland’s variational principle for vector-valued maps plays a key role. We also focus on improved Geoffrion proper it’s approximation characterize them through saddle point

In the traditional nonlinear optimization theory, Karush-Kuhn-Tucker (KKT) optimality conditions for constrained problems with inequality constraints play an essential role. The situation becomes challenging when theory of is discussed under uncertainty. Several researchers have interval approach to tackle uncertainty and derived conditions. However, there are several realistic situations in wh...

In this paper, the common centralized DEA models are extended to the bi-level centralized resource allocation (CRA) models based on revenue efficiency. Based on the Karush–Kuhn–Tucker (KKT) conditions, the bi-level CRA model is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). A recurrent neural network is developed for solving this one-level mathematica...

We solve saddle point problems by accelerated versions of the classical Cimmino’s method. For that, saddle point problems are reviewed and reformulated as best approximation problems. In that setting, low-cost optimization techniques are used for accelerating Cimmino’s method. Encouraging numerical results coming from KKT systems, Stokes problems and domain decomposition problems are presented....

Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Approximate KKT and Approximate Gradient Projection conditions are analyzed in this work. These conditions are not necessarily equivalent. Implications between different conditions and counter-examples will be shown. Algorithmic consequences will be discussed.

We prove local and global convergence results for an interior-point methodapplied to mathematical programs with equilibrium constraints. The globalresult shows the algorithm minimizes infeasibility regardless of startingpoint, while one result proves local convergence when penalty functions areexact; another local result proves convergence when the solution is not evena KKT point.