scholarly journals Duality Theorems for (ρ,ψ,d)-Quasiinvex Multiobjective Optimization Problems with Interval-Valued Components

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 894
Author(s):  
Savin Treanţă
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Integral Functional ◽  
Multiple Integral ◽  
Control Problems ◽  
Duality Theorems ◽  
New Class ◽  
Duality Results ◽  
Multiobjective Optimization Problems ◽  
Interval Valued

The present paper deals with a duality study associated with a new class of multiobjective optimization problems that include the interval-valued components of the ratio vector. More precisely, by using the new notion of (ρ,ψ,d)-quasiinvexity associated with an interval-valued multiple-integral functional, we formulate and prove weak, strong, and converse duality results for the considered class of variational control problems.

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.

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

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1473
Author(s):  
Savin Treanţă
Keyword(s):  
Optimization Problems ◽  
Integral Functional ◽  
Optimal Solution ◽  
Multiple Integral ◽  
Second Order ◽  
Control Problems ◽  
Mathematical Framework ◽  
Mixed Constraints ◽  
Scalar Multiple ◽  
Cost Functionals

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.

ϵ-Efficient solutions in semi-infinite multiobjective optimization

2018 ◽  
Vol 52 (4-5) ◽  
pp. 1397-1410
Author(s):  
Tatiana Shitkovskaya ◽  
Do Sang Kim
Keyword(s):  
Multiobjective Optimization ◽  
Nonsmooth Analysis ◽  
Constraint Qualification ◽  
Dual Problem ◽  
Optimization Problems ◽  
Efficient Solutions ◽  
Duality Theorems ◽  
Multiobjective Optimization Problems ◽  
Special Cases ◽  
Scalarization Method

In this paper we apply some tools of nonsmooth analysis and scalarization method due to Chankong–Haimes to find ϵ-efficient solutions of semi-infinite multiobjective optimization problems (MP). We establish ϵ-optimality conditions of Karush–Kuhn–Tucker (KKT) type under Farkas–Minkowski (FM) constraint qualification by using ϵ-subdifferential concept. In addition we propose mixed type dual problem (including dual problems of Wolfe and Mond–Weir types as special cases) for ϵ-efficient solutions and investigate relationship between mentioned (MP) and its dual problem as well as establish several ϵ-duality theorems.

scholarly journals Well Posedness of New Optimization Problems with Variational Inequality Constraints

2021 ◽  
Vol 5 (3) ◽  
pp. 123
Author(s):  
Savin Treanţă
Keyword(s):  
Variational Inequality ◽  
Lower Semicontinuity ◽  
Optimization Problems ◽  
Integral Functional ◽  
Inequality Constraints ◽  
Multiple Integral ◽  
Well Posedness ◽  
Constrained Optimization Problems ◽  
New Class ◽  
Theoretical Developments

In this paper, we studied the well posedness for a new class of optimization problems with variational inequality constraints involving second-order partial derivatives. More precisely, by using the notions of lower semicontinuity, pseudomonotonicity, hemicontinuity and monotonicity for a multiple integral functional, and by introducing the set of approximating solutions for the considered class of constrained optimization problems, we established some characterization results on well posedness. Furthermore, to illustrate the theoretical developments included in this paper, we present some examples.

Optimization of the mathematical programming and applications

2021 ◽  
Vol 2 (5) ◽  
pp. 7902-7911
Author(s):  
Johnny Moisés Valverde Montoro ◽  
Milton Milciades Cortez Gutiérrez ◽  
Hernán Oscar Cortez Gutiérrez
Keyword(s):  
Mathematical Programming ◽  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Kkt Conditions ◽  
Objective Functions ◽  
Multiobjective Optimization Problems ◽  
Interval Valued

The present investigation responds to the need to solve optimization problems with optimality conditions. The KKT conditions are considered for multiobjective optimization problems with interval-valued objective functions.

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.

scholarly journals Robust neutrosophic programming approach for solving intuitionistic fuzzy multiobjective optimization problems

2021 ◽  
Author(s):  
Firoz Ahmad
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Practical Implication ◽  
Real Life ◽  
Future Research ◽  
Programming Approach ◽  
Solution Approach ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multiobjective Optimization Problems

AbstractThis study presents the modeling of the multiobjective optimization problem in an intuitionistic fuzzy environment. The uncertain parameters are depicted as intuitionistic fuzzy numbers, and the crisp version is obtained using the ranking function method. Also, we have developed a novel interactive neutrosophic programming approach to solve multiobjective optimization problems. The proposed method involves neutral thoughts while making decisions. Furthermore, various sorts of membership functions are also depicted for the marginal evaluation of each objective simultaneously. The different numerical examples are presented to show the performances of the proposed solution approach. A case study of the cloud computing pricing problem is also addressed to reveal the real-life applications. The practical implication of the current study is also discussed efficiently. Finally, conclusions and future research scope are suggested based on the proposed work.

Sign in / Sign up

Export Citation Format

Share Document