Efficiency for variational control problems on Riemann manifolds with geodesic quasiinvex curvilinear integral functionals

2020 ◽  
Vol 114 (3) ◽  
Author(s):  
Savin Treanţă ◽  
Ştefan Mititelu
Keyword(s):  
Control Problems ◽  
Integral Functionals ◽  
Riemann Manifolds ◽  
Curvilinear Integral

scholarly journals Duality Results in Quasiinvex Variational Control Problems with Curvilinear Integral Functionals

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 811 ◽  
Author(s):  
Cipu
Keyword(s):  
Control Problems ◽  
Integral Functionals ◽  
Converse Duality ◽  
Duality Results ◽  
Curvilinear Integral

In this paper, we formulate and prove weak, strong and converse duality results invariational control problems involving (ρ,b)-quasiinvex path-independent curvilinear integralcost functionals.

scholarly journals On a Class of Isoperimetric Constrained Controlled Optimization Problems

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 112
Author(s):  
Savin Treanţă
Keyword(s):  
Boundary Conditions ◽  
Control Problem ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Control Problems ◽  
Integral Functionals ◽  
Curvilinear Integral ◽  
The One ◽  
Theoretical Results

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.

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

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 893
Author(s):  
Savin Treanţă
Keyword(s):  
Optimization Problems ◽  
Dual Pair ◽  
Control Problems ◽  
Integral Functionals ◽  
Duality Theorems ◽  
Converse Duality ◽  
New Class ◽  
Duality Results ◽  
Curvilinear Integral ◽  
Interval Valued

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 a class of variational-type inequalities involving curvilinear integral functionals

Optimization ◽  
2021 ◽  
pp. 1-19
Author(s):  
Savin Treană ◽  
Shipra Singh ◽  
Anurag Jayswal
Keyword(s):  
Integral Functionals ◽  
Curvilinear Integral ◽  
Variational Type

scholarly journals On Locally and Globally Optimal Solutions in Scalar Variational Control Problems

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 829 ◽  
Author(s):  
Savin Treanţă
Keyword(s):  
Control Problem ◽  
Optimal Solution ◽  
Control Problems ◽  
Optimal Solutions ◽  
Global Optimal Solution ◽  
New Class ◽  
Minimal Criterion ◽  
Local Optimal Solution ◽  
Global Optimal ◽  
Curvilinear Integral

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.

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

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1790
Author(s):  
Savin Treanţă ◽  
Koushik Das
Keyword(s):  
Saddle Point ◽  
Optimization Problems ◽  
Integral Functional ◽  
Optimal Solution ◽  
Control Problems ◽  
New Class ◽  
Mixed Constraints ◽  
Curvilinear Integral ◽  
Lagrange Functional ◽  
Cost 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.

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