On a Class of Isoperimetric Constrained Controlled Optimization Problems

Abstract

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.

Modern Problems of Mathematical Physics and Their Applications

“…The Lagrange dynamics generated by a class of isoperimetric constrained controlled optimization problems involving second-order partial derivatives and boundary conditions have been investigated by Treanţȃ in [13]. The author has derived necessary optimality conditions for the considered class of variational control problems governed by path-independent curvilinear integral functionals.…”

Well Posedness of New Optimization Problems with Variational Inequality Constraints

“…where D 2 βγ := D β (D γ ), and n(β, γ) is the Saunders's multi-index notation (see Saunders [41], Treanţȃ [40]).…”

“…Recently, the study of well posedness for vector variational inequalities and the associated optimization problems was formulated by Jayswal and Shalini [29]. On the other hand, an important and interesting extension of variational inequality problems is that of multidimensional variational inequality problems and the corresponding multi-time optimization problems (see [30][31][32][33][34][35][36][37][38][39][40]).…”

On Some Constrained Optimization Problems

“…More precisely, without limiting our investigation to convex costs as in Lee [16], the current framework is more comprehensive than in Schmitendorf [6], Hestenes [15], Udrişte and Ţevy [17], or Treanţȃ [2] both by the inclusion of integral functionals of multiple and curvilinear type as constraints and by the inclusion of new proofs. Additionally, compared with a very recent research paper (see Treanţȃ [18]), the present paper takes into account the isoperimetric constraints defined by multiple integral functionals (see Section 2.2). Moreover, due to the very important physical applications of the functionals used (for example, mechanical work), this paper is a very good starting point for researchers in the field of applied mathematics that deal with the design, theory, and applications of mathematics, management science, operations research, optimal control science, and economics.…”