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Search Results: 1 - 10 of 1092 matches for " ) convexity/pseudo-convexity "
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Non-differentiable second-order mixed symmetric duality with cone constraints
Shiv Kumar Gupta
Maejo International Journal of Science and Technology , 2012,
Abstract: A pair of mixed non-differentiable second-order symmetric dual programmesover cones is considered. Weak, strong and converse duality theorems are establishedunder second-order (F, ) convexity/pseudo-convexity assumptions. Special cases arealso discussed to show that this paper extends some known results in the literature.
A Gradient Method to Solve Multicriteria Optimization on Riemannian Manifolds

Pure Mathematics (PM) , 2016, DOI: 10.12677/PM.2016.61002


In this paper, we present a new gradient method in the Riemannian context to solve multicriteria optimization. If the objective function is quasiconvex, the sequence generated by this method converges to a critical Pareto point. If the objective function is pseudo-convex, then the sequence will converge to optimal Pareto point.

On second- order symmetric duality for a class of multiobjective fractional programming problem
Deo Brat Ojha
Tamkang Journal of Mathematics , 2012, DOI: 10.5556/j.tkjm.43.2012.267-279
Abstract: This article is concerned with a pair of second-order symmetric duals in the context of non-differentiable multiobjective fractional programming problems. We establish the weak and strong duality theorems for the new pair of dual models. Discussion on some special cases shows that results in this paper extend previous work in this area.
Tangent cones, starshape and convexity
J. M. Borwein
International Journal of Mathematics and Mathematical Sciences , 1978, DOI: 10.1155/s0161171278000460
Abstract: In the last few years various infinite dimensional extensions to Krasnoselski's Theorem on starshaped sets [14] have been made. These began with a paper by Edelstein and Keener [8] and have culminated in the papers by Borwein, Edelstein and O'Brien [3] [4] by Edelstein, Keener and O'Brien [9] and finally by O'Brien [16].
Minima Domain Intervals and the S-Convexity, as well as the Convexity, Phenomenon  [PDF]
I. M. R. Pinheiro
Advances in Pure Mathematics (APM) , 2012, DOI: 10.4236/apm.2012.26069
Abstract: In this paper, we propose a refinement in the analytical definition of the s2-convex classes of functions aiming to progress further in the direction of including s2-convexity properly in the body of Real Analysis.
First Note on the Definition of s1-Convexity  [PDF]
I. M. R. Pinheiro
Advances in Pure Mathematics (APM) , 2014, DOI: 10.4236/apm.2014.412076

In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.

A Simple Way to Prove the Characterization of Differentiable Quasiconvex Functions  [PDF]
Giorgio Giorgi
Applied Mathematics (AM) , 2014, DOI: 10.4236/am.2014.58114

We give a short and easy proof of the characterization of differentiable quasiconvex functions.

Second-order duality for nondifferentiable multiobjective programming involving (Φ,ρ)-univexity
Ganesh Kumar Thakur,Bandana Priya
Kathmandu University Journal of Science, Engineering and Technology , 2011, DOI: 10.3126/kuset.v7i1.5426
Abstract: The concepts of (Φ, ρ)-invexity have been given by Carsiti,Ferrara and Stefanescu[32]. We consider a second-order dual model associated to a multiobjective programming problem involving support functions and a weak duality result is established under appropriate second-order (Φ, ρ)-univexity conditions. AMS 2002 Subject Classification : 90C29; 90C30; 90C46. Key words : Second-order (Φ, ρ)-(pseudo/quasi)-convexity; multiobjective programming; second-order duality; duality theorem. DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5426 KUSET 2011; 7(1): 92-104 ?
Some Properties on the Function Involving the Gamma Function  [PDF]
Bin Chen
Applied Mathematics (AM) , 2012, DOI: 10.4236/am.2012.36090
Abstract: We studied the monotonicity and Convexity properties of the new functions involving the gamma function, and get the general conclusion that Minc-Sathre and C. P. Chen-G. Wang’s inequality are extended and refined.
Second-Order Duality for Nondifferentiable Multiobjective Programming Involving (φ, ρ)-Univexity
Deo Brat Ojha
Research Journal of Applied Sciences, Engineering and Technology , 2010,
Abstract: The concepts of (&phi, ρ)-invexity have been introduced by Carsiti, Ferrara and Stefanescu. We consider a second-order dual model associated to a multiobjective programming problem involving support functions and a weak duality result is established under appropriate second-order (&phi, ρ)-univexity conditions.
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