On second-order converse duality for a nondifferentiable programming problem

2005 ◽  
Vol 72 (2) ◽  
pp. 265-270 ◽  
Author(s):  
Xin Min Yang ◽  
Ping Zhang
Keyword(s):  
Programming Problem ◽  
Recent Work ◽  
Second Order ◽  
Nondifferentiable Programming ◽  
Converse Duality ◽  
Duality Results

Certain shortcomings are described in the second order converse duality results in the recent work of (J. Zhang and B. Mond, Bull. Austral. Math. Soc. 55(1997) 29–44). Appropriate modifications are suggested.

Duality relations for second-order programming problem under (G,αf)-bonvexity assumptions

2018 ◽  
Vol 13 (02) ◽  
pp. 2050044 ◽  
Author(s):  
Ramu Dubey ◽  
Vishnu Narayan Mishra ◽  
Puneet Tomar
Keyword(s):  
Programming Problem ◽  
Duality Theorem ◽  
Optimization Problem ◽  
Second Order ◽  
Dual Model ◽  
Weak Duality ◽  
Numerical Examples ◽  
Duality Results ◽  
Duality Relations ◽  
Definition Of

In this paper, we introduce the definition of [Formula: see text]-bonvex/[Formula: see text]-pseudobonvex functions and to show the existence of such functions, we construct nontrivial numerical examples. In the next section, we formulate a pair of second-order symmetric dual model in optimization problem and proved the duality results under [Formula: see text]-bonvexity/[Formula: see text]-pseudobonvexity assumptions. Further, we also construct nontrivial concrete examples which justifying definitions as well as the weak duality theorem presented in the paper.

Symmetric duality results for second-order nondifferentiable multiobjective programming problem

2019 ◽  
Vol 53 (2) ◽  
pp. 539-558 ◽  
Author(s):  
Ramu Dubey ◽  
Vishnu Narayan Mishra
Keyword(s):  
Programming Problem ◽  
Duality Theorem ◽  
Multiobjective Programming ◽  
Second Order ◽  
Weak Duality ◽  
Symmetric Duality ◽  
Numerical Examples ◽  
Duality Results ◽  
Duality Relations ◽  
Multiobjective Programming Problem

In this article, we study the existence of Gf-bonvex/Gf -pseudo-bonvex functions and construct various nontrivial numerical examples for the existence of such type of functions. Furthermore, we formulate Mond-Weir type second-order nondifferentiable multiobjective programming problem and give a nontrivial concrete example which justify weak duality theorem present in the paper. Next, we prove appropriate duality relations under aforesaid assumptions.

scholarly journals Mond-Weir type second order multiobjective mixed symmetric duality with square root term under generalized univex function

2013 ◽  
Vol 4 (1) ◽  
pp. 21-33
Author(s):  
Arun Kumar Tripathy
Keyword(s):  
Second Order ◽  
Nondifferentiable Programming ◽  
Square Root ◽  
Symmetric Duality ◽  
New Class ◽  
Duality Results ◽  
Special Cases ◽  
Mild Assumption ◽  
Root Term

In this paper, a new class of second order (Φ,ρ)-univex and second order (Φ,ρ)-pseudo univex function are introduced with example. A pair Mond-Weir type second order mixed symmetric duality for multiobjective nondifferentiable programming is formulated and the duality results are established under the mild assumption of second order (∅,ρ) univexity and second order pseudo univexity. Special cases are discussed to show that this study extends some of the known results in related domain..

scholarly journals Sufficiency and duality of set-valued fractional programming problems via second-order contingent epiderivative

2021 ◽  
pp. 19-19
Author(s):  
Koushik Das
Keyword(s):  
Optimality Conditions ◽  
Programming Problem ◽  
Fractional Programming ◽  
Second Order ◽  
Primal Problem ◽  
Duality Results ◽  
Contingent Epiderivative ◽  
Convexity Assumptions ◽  
Mixed Types ◽  
Cone Convexity

In this paper, we establish second-order sufficient KKT optimality conditions of a set-valued fractional programming problem under second-order generalized cone convexity assumptions. We also prove duality results between the primal problem and second-order dual problems of parametric, Mond-Weir, Wolfe, and mixed types via the notion of second-order contingent epiderivative.

Autonomie, Charakter und praktische Vernunft: Überlegungen am Beispiel des Utilitarismus

1999 ◽  
Vol 21 (2) ◽  
Author(s):  
R. Jay Wallace
Keyword(s):  
Recent Work ◽  
Moral Agent ◽  
Second Order ◽  
Bernard Williams ◽  
Personal Projects ◽  
Peter Railton ◽  
Order Reflection

AbstractThis paper explores the question whether utilitarianism is compatible with the autonomy of the moral agent. The paper begins by considering Bernard Williams' famous complaint that utilitarianism cannot do justice to the personal projects and commitments constitutive of character. Recent work (by Peter Railton among others) has established that a utilitarian agent need not be free of such personal projects and commitments, and could even affirm them morally at the level of second"order reflection. But a different and more subtle problem confronts this approach: the use of utilitarian principles to justify the cultivation of personal projects and attachments undermines the autonomy to support this objection, according to which autonomy is a matter of acting in a way one can reflectively endorse.

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