On well-posedness associated with a class of controlled variational inequalities

In this paper, by using the new concepts of monotonicity, pseudomonotonicity and hemicontinuity associated with the considered curvilinear integral functional, we investigate the well-posedness and well-posedness in generalized sense for a class of controlled variational inequality problems. More precisely, by introducing the approximating solution set of the considered class of controlled variational inequality problems, we formulate and prove some characterization results on well-posedness and well-posedness in generalized sense. Also, the theoretical developments presented in the paper are accompanied by illustrative examples.

On Robust Saddle-Point Criterion in Optimization Problems with Curvilinear Integral Functionals

In this paper, we introduce a new class of multi-dimensional robust optimization problems (named (P)) with mixed constraints implying second-order partial differential equations (PDEs) and inequations (PDIs). Moreover, we define an auxiliary (modified) class of robust control problems (named (P)(b¯,c¯)), which is much easier to study, and provide some characterization results of (P) and (P)(b¯,c¯) by using the notions of normal weak robust optimal solution and robust saddle-point associated with a Lagrange functional corresponding to (P)(b¯,c¯). For this aim, we consider path-independent curvilinear integral cost functionals and the notion of convexity associated with a curvilinear integral functional generated by a controlled closed (complete integrable) Lagrange 1-form.

On a Class of Isoperimetric Constrained Controlled Optimization Problems

In this paper, we investigate the Lagrange dynamics generated by a class of isoperimetric constrained controlled optimization problems involving second-order partial derivatives and boundary conditions. More precisely, we derive necessary optimality conditions for the considered class of variational control problems governed by path-independent curvilinear integral functionals. Moreover, the theoretical results presented in the paper are accompanied by an illustrative example. Furthermore, an algorithm is proposed to emphasize the steps to be followed to solve a control problem such as the one studied in this paper.

On a Dual Pair of Multiobjective Interval-Valued Variational Control Problems

In this paper, by using the new concept of (ϱ,ψ,ω)-quasiinvexity associated with interval-valued path-independent curvilinear integral functionals, we establish some duality results for a new class of multiobjective variational control problems with interval-valued components. More concretely, we formulate and prove weak, strong, and converse duality theorems under (ϱ,ψ,ω)-quasiinvexity hypotheses for the considered class of optimization problems.

On Locally and Globally Optimal Solutions in Scalar Variational Control Problems

In this paper, optimality conditions are studied for a new class of PDE and PDI-constrained scalar variational control problems governed by path-independent curvilinear integral functionals. More precisely, we formulate and prove a minimal criterion for a local optimal solution of the considered PDE and PDI-constrained variational control problem to be its global optimal solution. The effectiveness of the main result is validated by a two-dimensional non-convex scalar variational control problem.