Results 21 to 30 of about 431 (190)

On the Continuity of the Kernel of Invex Functions [PDF]

Journal of Mathematical Analysis and Applications, 1996
A differentiable real function is invex on a domain \(C\) if \(f(x)- f(u) \geq\eta(x,u)^T \nabla f(u)\) for all \(x,u\) in \(C\). Examples are given where the kernel \(\eta(.,.)\) is required to be continuous; and sufficient conditions are obtained for a continuous \(\eta\) to exist, or to not exist.
Smart, Ian
openaire   +3 more sources

Modified Courant-Beltrami penalty function and a duality gap for invex optimization problem [PDF]

International Journal for Simulation and Multidisciplinary Design Optimization, 2019
In this paper, we modified a Courant-Beltrami penalty function method for constrained optimization problem to study a duality for convex nonlinear mathematical programming problems. Karush-Kuhn-Tucker (KKT) optimality conditions for the penalized problem
Hassan Mansur, Baharum Adam
doaj   +2 more sources

Nonsmooth Invex Functions and Sufficient Optimality Conditions [PDF]

Journal of Mathematical Analysis and Applications, 2001
The author unifies various definitions of non-smooth invex functions by introducing the \(K\)-directional derivative of a function in the following way. Let \(X\subset\mathbb{R}^n\) be an open set, \(f:X\to\mathbb{R}\), \(x\in X\) and \(K\) be a local cone approximation; the positive homogeneous function \(f^K(x,.): \mathbb{R}^n\to [-\infty,\infty ...
Castellani, Marco
openaire   +4 more sources

Optimality Condition and Wolfe Duality for Invex Interval-Valued Nonlinear Programming Problems [PDF]

Journal of Applied Mathematics, 2013
The concepts of preinvex and invex are extended to the interval-valued functions. Under the assumption of invexity, the Karush-Kuhn-Tucker optimality sufficient and necessary conditions for interval-valued nonlinear programming problems are derived ...
Jianke Zhang
doaj   +2 more sources

On nonsmooth multiobjective fractional programming problems involving (p, r)− ρ −(η ,θ)- invex functions [PDF]

Yugoslav Journal of Operations Research, 2013
A class of multiobjective fractional programming problems (MFP) is considered where the involved functions are locally Lipschitz. In order to deduce our main results, we introduce the definition of (p,r)−ρ −(η,θ)-invex class about the Clarke ...
Jayswal Anurag, Prasad Ashish Kumar, Stancu-Minasian I.M.   +2 more
doaj   +3 more sources

Geodesic B-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds [PDF]

Journal of Applied Mathematics, 2014
We introduce a class of functions called geodesic B-preinvex and geodesic B-invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo B-preinvex and geodesic quasi/pseudo B-invex functions.
Sheng-lan Chen, Nan-Jing Huang, Donal O'Regan   +2 more
doaj   +2 more sources

Inequalities for H-invex functions with applications for uniformly convex and superquadratic functions [PDF]

Filomat, 2017
In this paper, we introduce and study H-invex functions including the classes of convex, ?-invex, (F,G)-invex, c-strongly convex, ?-uniformly convex and superquadratic functions, respectively. Each Hinvex function attains its global minimum at an H-stationary point.
Marek Niezgoda
openaire   +3 more sources

A Study of Geodesic (E, F)-Preinvex Functions on Riemannian Manifolds [PDF]

Mathematics
In this manuscript, we define the (E,F)-invex set, (E,F)-invex functions, and (E,F)-preinvex functions on Euclidean space, i.e., simply vector space. We extend these concepts on the Riemannian manifold.
Ehtesham Akhter, Mohd Bilal, Musavvir Ali   +2 more
doaj   +2 more sources

Further Study on Strong Lagrangian Duality Property for Invex Programs via Penalty Functions [PDF]

Journal of Inequalities and Applications, 2010
We apply the quadratic penalization technique to derive strong Lagrangian duality property for an inequality constrained invex program. Our results extend and improve the corresponding results in the literature.
Huang XX, Zhang J
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Higher-Order Wolfe Type Symmetric Fractional Programming Problem Under Generalized Assumptions [PDF]

International Journal of Mathematical, Engineering and Management Sciences, 2022
The Wolfe-type model over arbitrary cones is a new sort of model that we introduce in this article. We defend duality theorems under more generalized higher-order assumptions in the section after this.
Rajnish Kumar, Khursheed Alam, Ramu Dubey   +2 more
doaj   +1 more source