Multitime multiobjective variational problems and vector variational-like inequalities

KT‐pseudoinvex multidimensional control problem

“…In this paper, following the control and variational problems considered in the works of Mititelu, Udrişte and Ţevy, Treanţă,() Jayswal et al, and Antczak and Pitea, as a natural continuation of these, we introduce a new class of control problems governed by multiple integrals and m ‐flow type partial differential equation (PDE) constraints. More precisely, we consider a multidimensional control problem of minimizing a multiple‐integral cost functional subject to nonlinear equality and inequality constraints involving first‐order partial derivatives.…”

“…Udrişte 21 and Rapcsák 22 proposed a generalization of convexity on manifolds, and Pini 23 introduced the notion of invex function on Riemannian manifolds. Other approaches have been well documented in the works of Barani and Pouryayevali 24 and Agarwal et al 25 In this paper, following the control and variational problems considered in the works of Mititelu, 26 Udrişte andŢevy, 27 Treanţȃ, 28-30 Jayswal et al, and 31 Antczak and Pitea, 32 as a natural continuation of these, we introduce a new class of control problems governed by multiple integrals and m-flow type partial differential equation (PDE) constraints. More precisely, we consider a multidimensional control problem of minimizing a multiple-integral cost functional subject to nonlinear equality and inequality constraints involving first-order partial derivatives.…”

Multi-Time Generalized Nash Equilibria with Dynamic Flow Applications

“…Taking into account the definitions of generalized convexities formulated in [32,33], we define the following notion of convexity for a multi-time functional H : K → R of the form H(x(t)) = Ω l•,l 1 h(x(s))ds, where h is a real-valued continuously differentiable function.…”

On Weak Variational Control Inequalities via Interval Analysis

“…Additionally, Liu [7] studied variational inequalities and optimization problems, and Treanţȃ [8] contributed to the study of vector variational inequalities and multiobjective optimization problems. Jayswal et al [9] formulated and proved some results for multiple objective optimization problems and vector variational inequalities. Connections between the solutions of some interval-valued multiple objective optimization problems and vector variational inequalities have been derived by Zhang et al [10].…”