On generalized semi-infinite programming - Discussion

Date

2006-06-01

Author

Weber, Gerhard Wilhelm
Tezel, A.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

162
views

0
downloads

This paper surveys some basic properties of the class of generalized semi-infinite programming problems (GSIP) where the infinite index set of inequality constraints depends on the state variables and all emerging functions are assumed to be continuously differentiable. There exists a wide range of applications which can be modelled as a (GSIP). The paper discusses extensions of the Mangasarian-Fromovitz, Kuhn-Tucker and Abadie constraint qualification to (GSIP) and presents related first order optimality conditions of Fritz-John and Karush-Kuhn-Tucker type. By using directional differentiability properties of the optimal value function of the lower level problem, first and second order necessary and sufficient optimality conditions are discussed. Several examples illustrate the results presented. Key Words: Generalized semi-infinite programming, extended Mangasarian-Fromovitz, Kuhn-Tucker and Abadie constraint qualification, Fritz-John condition, first and second order optimality conditions, optimal value function, directional differentiability, second order epiregularity, second order growth condition.

Subject Keywords

Gene-expression

URI

https://hdl.handle.net/11511/54913

Journal

TOP

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

Almost periodic solutions of the linear differential equation with piecewise constant argument Akhmet, Marat (2009-10-01) The paper is concerned with the existence and stability of almost periodic solutions of linear systems with piecewise constant argument where t∈R, x ∈ Rn [·] is the greatest integer function. The Wexler inequality [1]-[4] for the Cauchy's matrix is used. The results can be easily extended for the quasilinear case. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Copyright © 2009 Watam Press.
On decoding interleaved reed-solomon codes Yayla, Oğuz; Özbudak, Ferruh; Department of Cryptography (2011) Probabilistic simultaneous polynomial reconstruction algorithm of Bleichenbacher-Kiayias-Yung is extended to the polynomials whose degrees are allowed to be distinct. Furthermore, it is observed that probability of the algorithm can be increased. Specifically, for a finite field $\F$, we present a probabilistic algorithm which can recover polynomials $p_1,\ldots, p_r \in \F[x]$ of degree less than $k_1,k_2,\ldots,k_r$, respectively with given field evaluations $p_l(z_i) = y_{i,l}$ for all $i \in I$, $
On periodic solutions of linear impulsive delay differential systems Akhmet, Marat; Alzabut, J.O.; Zafer, Ağacık (2008-10-01) A necessary and sufficient condition is established for the existence of periodic solutions of linear impulsive delay differential systems. Copyright © 2008 Watam Press.
Exponential stability of periodic solutions of recurrent neural networks with functional dependence on piecewise constant argument Akhmet, Marat; Cengiz, Nur (null; 2015-08-25) Akhmet [1] generalized differential equations with piecewise constant argument by taking any piecewise constant functions as arguments, and recently he introduced functional dependence on piecewise constant argument [2]. These equations play an important role in applications such as neural networks [3]. In this study, we develope a model of recurrent neural network with functional dependence on piecewise constant argument of generalized type given by x 0 (t) = −Ax (t) + Ex (γ (t)) + Bh (xt) + Cg xγ(t) + D...
Exponentially dichotomous linear systems of differential equations with piecewise constant argument Akhmet, Marat (2012-01-01) © 2012 L & H Scientific Publishing, LLC.We consider differential equations with piecewise constant argument of generalized type. It is the first time, an attention is given to the exponential dichotomy of linear systems. Bounded, almost periodic and periodic solutions and their stability are discussed. The study is made in such a way that further construction of the theory will follow for ordinary differential equations. The results are illustrated by examples.

Citation Formats

G. W. Weber and A. Tezel, “On generalized semi-infinite programming - Discussion,” TOP, pp. 48–55, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54913.