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

Minty Variational Principle for Nonsmooth Interval-Valued Vector Optimization Problems on Hadamard Manifolds

This article deals with the classes of approximate Minty- and Stampacchia-type vector variational inequalities on Hadamard manifolds and a class of nonsmooth interval-valued vector optimization problems. By using the Clarke subdifferentials, we define a new class of functions on Hadamard manifolds, namely, the geodesic LU-approximately convex functions. Under geodesic LU-approximate convexity hypothesis, we derive the relationship between the solutions of these approximate vector variational inequalities and nonsmooth interval-valued vector optimization problems. This paper extends and generalizes some existing results in the literature.

Semidefinite Multiobjective Mathematical Programming Problems with Vanishing Constraints Using Convexificators

In this paper, we establish Fritz John stationary conditions for nonsmooth, nonlinear, semidefinite, multiobjective programs with vanishing constraints in terms of convexificator and introduce generalized Cottle type and generalized Guignard type constraints qualification to achieve strong S—stationary conditions from Fritz John stationary conditions. Further, we establish strong S—stationary necessary and sufficient conditions, independently from Fritz John conditions. The optimality results for multiobjective semidefinite optimization problem in this paper is related to two recent articles by Treanta in 2021. Treanta in 2021 discussed duality theorems for special class of quasiinvex multiobjective optimization problems for interval-valued components. The study in our article can also be seen and extended for the interval-valued optimization motivated by Treanta (2021). Some examples are provided to validate our established results.

On a Class of Second-Order PDE&PDI Constrained Robust Modified Optimization Problems

In this paper, by using scalar multiple integral cost functionals and the notion of convexity associated with a multiple integral functional driven by an uncertain multi-time controlled second-order Lagrangian, we develop a new mathematical framework on multi-dimensional scalar variational control problems with mixed constraints implying second-order partial differential equations (PDEs) and inequations (PDIs). Concretely, we introduce and investigate an auxiliary (modified) variational control problem, which is much easier to study, and provide some equivalence results by using the notion of a normal weak robust optimal solution.