scholarly journals Mathematical programming involving (α, p)-right upper-Dini-derivative functions

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 899-908 ◽  
Author(s):  
Dehui Yuan ◽  
Xiaoling Liu
Keyword(s):  
Mathematical Programming ◽  
Directional Derivative ◽  
Efficient Solutions ◽  
Sufficient Optimality Conditions ◽  
Generalized Convex Functions ◽  
Dini Derivative ◽  
Duality Results ◽  
Multi Objective Programming ◽  
Pareto Efficient ◽  
Generalized Convexities

In this paper, we give some new generalized convexities with the tool-right upper-Dini-derivative which is an extension of directional derivative. Next, we establish not only Karush-Kuhn-Tucker necessary but also sufficient optimality conditions for mathematical programming involving new generalized convex functions. In the end, weak, strong and converse duality results are proved to relate weak Pareto (efficient) solutions of the multi-objective programming problems (VP), (MVD) and (MWD).

scholarly journals Interval-Valued Optimization Problems Involvingα,ρ-Right Upper-Dini-Derivative Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Vasile Preda
Keyword(s):  
Optimization Problems ◽  
Directional Derivative ◽  
Efficient Solutions ◽  
Sufficient Optimality Conditions ◽  
Dini Derivative ◽  
Duality Results ◽  
Multiobjective Problem ◽  
Necessary And Sufficient ◽  
Generalized Convexities ◽  
Interval Valued

We consider an interval-valued multiobjective problem. Some necessary and sufficient optimality conditions for weak efficient solutions are established under new generalized convexities with the tool-right upper-Dini-derivative, which is an extension of directional derivative. Also some duality results are proved for Wolfe and Mond-Weir duals.

scholarly journals Optimality and Duality for Nondifferentiable Minimax Fractional Programming with Generalized Convexity

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Anurag Jayswal
Keyword(s):  
Fractional Programming ◽  
Generalized Convexity ◽  
Optimality Criteria ◽  
Sufficient Optimality Conditions ◽  
View Point ◽  
Generalized Convex Functions ◽  
Duality Results ◽  
Minimax Fractional Programming ◽  
Optimality And Duality ◽  
Dual Models

We establish several sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems from a view point of generalized convexity. Subsequently, these optimality criteria are utilized as a basis for constructing dual models, and certain duality results have been derived in the framework of generalized convex functions. Our results extend and unify some known results on minimax fractional programming problems.

scholarly journals Optimality condition and duality in multi objective programming with generalized (φ,ρ)-univexity

1970 ◽  
Vol 7 (1) ◽  
pp. 105-112
Author(s):  
Deo Brat Ojha
Keyword(s):  
Efficient Solution ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Sufficient Optimality Conditions ◽  
Type I ◽  
Duality Results ◽  
Multi Objective Programming ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Generalized Type

In this paper, we extend the classes of generalized type I vector valued functions introduced by Aghezzaf and Hachimi[1] to generalized univex type I vector-valued functions and consider a multiobjective optimization problem involving generalized type I function with (φ,r ) -univexity. A number of Kuhn-Tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution. The Mond-Weir and general Mond-Weir type duality results are also presented. DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5427 KUSET 2011; 7(1): 105-112

scholarly journals Sufficient optimality conditions and Mond-Weir duality results for a fractional multiobjective optimization problem

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Nazih Abderrazzak Gadhi ◽  
Fatima Zahra Rahou
Keyword(s):  
Multiobjective Optimization ◽  
Optimality Conditions ◽  
Optimization Problem ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Multiobjective Optimization Problem ◽  
Support Functions ◽  
Duality Results ◽  
The Given ◽  
Generalized Convexities

<p style='text-indent:20px;'>In this work, we are concerned with a fractional multiobjective optimization problem <inline-formula><tex-math id="M1">\begin{document}$ (P) $\end{document}</tex-math></inline-formula> involving set-valued maps. Based on necessary optimality conditions given by Gadhi et al. [<xref ref-type="bibr" rid="b14">14</xref>], using support functions, we derive sufficient optimality conditions for <inline-formula><tex-math id="M2">\begin{document}$ \left( P\right) , $\end{document}</tex-math></inline-formula> and we establish various duality results by associating the given problem with its Mond-Weir dual problem <inline-formula><tex-math id="M3">\begin{document}$ \left( D\right) . $\end{document}</tex-math></inline-formula> The main tools we exploit are convexificators and generalized convexities. Examples that illustrates our findings are also given.</p>

A MULTICRITERIA DECISION SUPPORT SYSTEM FOR COMPETENCE-DRIVEN PROJECT PORTFOLIO SELECTION

2009 ◽  
Vol 08 (02) ◽  
pp. 379-401 ◽  
Author(s):  
CHRISTIAN STUMMER ◽  
ELMAR KIESLING ◽  
WALTER J. GUTJAHR
Keyword(s):  
Decision Support ◽  
Decision Support System ◽  
Support System ◽  
Efficient Solutions ◽  
Project Portfolio ◽  
Practical Application ◽  
Multicriteria Decision ◽  
Pareto Efficient ◽  
Conducting Research ◽  
Multicriteria Decision Support

The systematic and proactive development of human resources is of major importance in organizations that rely heavily on the competencies of their employees when engaging in innovative endeavors. Human capital, however, is not only a resource required for conducting research, but also the eventual result of that research. When selecting a research portfolio, the decision-maker (DM) thus needs to take into consideration both current and future competence requirements, as well as other financial and nonfinancial objectives and constraints. We introduce a proper multicriteria decision support system (MCDSS) that first determines the set of Pareto-efficient solutions and then allows the DM to interactively filter and/or explore this set in various ways. Its practical application is demonstrated by means of a showcase at the Electronic Commerce Competence Center (EC3) in Vienna, Austria.

scholarly journals Continuous programming containing arbitrary norms

1985 ◽  
Vol 39 (1) ◽  
pp. 28-38 ◽  
Author(s):  
S. Chandra ◽  
B. D. Craven ◽  
I. Husain
Keyword(s):  
Mathematical Programming ◽  
Constrained Optimization ◽  
Optimality Conditions ◽  
Duality Result ◽  
Duality Results ◽  
Continuous Programming ◽  
Arbitrary Norms ◽  
Abstract Spaces ◽  
Special Case

AbstractOptimality conditions and duality results are obtained for a class of cone constrained continuous programming problems having terms with arbitrary norms in the objective and constraint functions. The proofs are based on a Fritz John theorem for constrained optimization in abstract spaces. Duality results for a fractional analogue of such continuous programming problems are indicated and a nondifferentiable mathematical programming duality result, not explicitly reported in the literature, is deduced as a special case.

scholarly journals Sufficient optimality criteria and duality for variational problems with generalised invexity

1989 ◽  
Vol 31 (1) ◽  
pp. 108-121 ◽  
Author(s):  
B. Mond ◽  
I. Husain
Keyword(s):  
Mathematical Programming ◽  
Variational Problems ◽  
Optimality Criteria ◽  
Duality Results

AbstractA number of Kuhn-Tucker type sufficient optimality criteria for a class of variational problems under weaker invexity assumptions are presented. As an application of these optimality results, various Mond-Weir type duality results are proved under a variety of generalised invexity assumptions. These results generalise many well-known duality results of variational problems and also give a dynamic analogue of certain corresponding (static) results relating to duality with generalised invexity in mathematical programming.

scholarly journals Optimality and duality for nonsmooth semi-infinite E-convex multi-objective programming with support functions

2020 ◽  
Vol 11 ◽  
pp. 17
Author(s):  
Tarek Emam
Keyword(s):  
Strong Duality ◽  
Sufficient Optimality Conditions ◽  
Convex Programming Problem ◽  
Duality Theorems ◽  
Support Functions ◽  
Primal Problem ◽  
Multi Objective ◽  
Multi Objective Programming ◽  
Optimality And Duality ◽  
Convexity Assumptions

In this paper, we study a nonsmooth semi-infinite multi-objective E-convex programming problem involving support functions. We derive sufficient optimality conditions for the primal problem. We formulate Mond-Weir type dual for the primal problem and establish weak and strong duality theorems under various generalized E-convexity assumptions.

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