共查询到20条相似文献,搜索用时 46 毫秒
1.
Vsevolod I. Ivanov 《Journal of Global Optimization》2010,46(1):31-47
In this article we introduce the notions of Kuhn-Tucker and Fritz John pseudoconvex nonlinear programming problems with inequality
constraints. We derive several properties of these problems. We prove that the problem with quasiconvex data is (second-order)
Kuhn-Tucker pseudoconvex if and only if every (second-order) Kuhn-Tucker stationary point is a global minimizer. We obtain
respective results for Fritz John pseudoconvex problems. For the first-order case we consider Fréchet differentiable functions
and locally Lipschitz ones, for the second-order case Fréchet and twice directionally differentiable functions. 相似文献
2.
Abdelghani OUAHAB 《数学学报(英文版)》2008,24(1):95-106
A recent nonlinear alternative for contraction maps in Frechet spaces due to Frigon and Granas (Resultats de type Leray-Schauder pour des contractions sur des espaces de Frechet, Ann. Sci. Math. Quebec 22, (2), 161-168 (1998)), combined with semigroup theory, is used to investigate the existence and uniqueness of mild solutions for first- and second-order functional semi linear and neutral damped differential equations in Frechet space. 相似文献
3.
We show that in two dimensions or higher, the Mordukhovich-Ioffe approximate subdifferential and Clarke subdifferential may differ almost everywhere for real-valued Lipschitz functions. Uncountably many Fréchet differentiable vector-valued Lipschitz functions differing by more than constants can share the same Mordukhovich-Ioffe coderivatives. Moreover, the approximate Jacobian associated with the Mordukhovich-Ioffe coderivative can be nonconvex almost everywhere for Fréchet differentiable vector-valued Lipschitz functions. Finally we show that for vector-valued Lipschitz functions the approximate Jacobian associated with the Mordukhovich-Ioffe coderivative can be almost everywhere disconnected. 相似文献
4.
I. P. Ryazantseva 《Russian Mathematics (Iz VUZ)》2016,60(11):45-57
In a Hilbert space we construct a regularized continuous analog of the Newton method for nonlinear equation with a Fréchet differentiable and monotone operator. We obtain sufficient conditions of its strong convergence to the normal solution of the given equation under approximate assignment of the operator and the right-hand of the equation. 相似文献
5.
In this article, a recent nonlinear alternative for contraction maps in Fréchet spaces due to Frigon and Granas [1998, Résultats de type Leray-Schauder pour des contractions sur des espaces de Fréchet, Ann. Sci. Math. Québec 22, 161–168] is used to investigate the existence and uniqueness of solutions for fractional order functional differential equations with infinite delay. 相似文献
6.
《Optimization》2012,61(5):489-503
We introduce a notion of a second-order invex function. A Fréchet differentiable invex function without any further assumptions is second-order invex. It is shown that the inverse claim does not hold. A Fréchet differentiable function is second-order invex if and only if each second-order stationary point is a global minimizer. Two complete characterizations of these functions are derived. It is proved that a quasiconvex function is second-order invex if and only if it is second-order pseudoconvex. Further, we study the nonlinear programming problem with inequality constraints whose objective function is second-order invex. We introduce a notion of second-order type I objective and constraint functions. This class of problems strictly includes the type I invex ones. Then we extend a lot of sufficient optimality conditions with generalized convex functions to problems with second-order type I invex objective function and constraints. Additional optimality results, which concern type I and second-order type I invex data are obtained. An answer to the question when a kernel, which is not identically equal to zero, exists is given. 相似文献
7.
《Optimization》2012,61(12):2117-2137
ABSTRACTIn this paper, we study a vector optimization problem (VOP) with both inequality and equality constraints. We suppose that the functions involved are Fréchet differentiable and their Fréchet derivatives are continuous or stable at the point of study. By virtue of a second-order constraint qualification of Abadie type, we provide second-order Karush–Kuhn–Tucker type necessary optimality conditions for the VOP. Moreover, we also obtain second-order sufficient optimality conditions for a kind of strict local efficiency. Both the necessary conditions and the sufficient conditions are shown in equivalent pairs of primal and dual formulations by using theorems of the alternative for the VOP. 相似文献
8.
We study a multiobjective optimization program with a feasible set defined by equality constraints and a generalized inequality
constraint. We suppose that the functions involved are Fréchet differentiable and their Fréchet derivatives are continuous
or stable at the point considered. We provide necessary second order optimality conditions and also sufficient conditions
via a Fritz John type Lagrange multiplier rule and a set-valued second order directional derivative, in such a way that our
sufficient conditions are close to the necessary conditions. Some consequences are obtained for parabolic directionally differentiable
functions and C
1,1 functions, in this last case, expressed by means of the second order Clarke subdifferential. Some illustrative examples are
also given. 相似文献
9.
Necessary conditions for the optimality of a pair with respect to a locally Lipschitz cost functional L(y,u) , subject to Ay + F(y) = Cu + B(u) , are given in terms of generalized gradients. Here A and C are densely defined, closed, linear operators on some Banach spaces, while F and B are (Fréchet) differentiable maps, which are suitably related to A and C . Various examples and potential applications to nonlinear programming models and nonlinear optimal control of partial differential
equations are also discussed.
Accepted 18 March 1998 相似文献
10.
We present several formulae for the proximal and Fréchet subdifferentials of the minimal time function defined by a linear
control system and a target set. At every point inside the target set, the proximal/Fréchet subdifferential is the intersection
of the proximal/Fréchet normal cone of the target set and an upper level set of a so-called Hamiltonian function which depends
only on the linear control system. At every point outside the target set, under a mild assumption, proximal/Fréchet subdifferential
is the intersection of the proximal/Fréchet normal cone of an enlargement of the target set and a level set of the Hamiltonian
function. 相似文献
11.
New fixed point theorems for maps (single and multivalued) between Fréchet spaces are presented. The proof relies on fixed point theory in Banach spaces and viewing a Fréchet space as the projective limit of a sequence of Banach spaces. 相似文献
12.
Petr Hájek 《Israel Journal of Mathematics》1998,107(1):237-252
We show that every Fréchet differentiable real function onC(K), K scattered with locally uniformly continuous derivative has locally compact derivative. Using this and similar results, we
investigate the existence ofC
2-Fréchet smooth surjections between various Banach spaces. 相似文献
13.
《Nonlinear Analysis: Theory, Methods & Applications》2005,61(3):405-423
In this paper, a recent nonlinear alternative for multivalued admissible contractions in Fréchet spaces due to Frigon combined with semigroups theory is used to investigate the controllability of some classes of semilinear functional and neutral functional differential inclusions in Fréchet spaces. 相似文献
14.
M. Chen Y. Khan Q. Wu A. Yildirim 《Journal of Optimization Theory and Applications》2013,157(3):651-662
A Newton–Kantorovich convergence theorem of a modified Newton’s method having third order convergence is established under the gamma-condition in a Banach space to solve nonlinear equations. It is assumed that the nonlinear operator is twice Fréchet differentiable and satisfies the gamma-condition. We also present the error estimate to demonstrate the efficiency of our approach. A comparison of our numerical results with those obtained by other Newton–Kantorovich convergence theorems shows high accuracy of our results. 相似文献
15.
T. Konderla 《Mathematical Notes》2012,91(1-2):65-68
We describe a construction of convex functions on infinite-dimensional spaces and apply this construction to give an illustration to a theorem of Borwein-Fabian from [1]. Namely, we give a simple explicit example of a continuous convex function on l p , p ≥ 1, which is everywhere compactly differentiable, but not Fréchet differentiable at zero. 相似文献
16.
In this article we present new Lefschetz fixed point theorems for compact absorbing contractive admissible maps between Fréchet spaces. Also, we discuss condensing maps with a compact attractor. Finally we present new antipodal fixed point theory for Kakutani maps. 相似文献
17.
A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fréchet distance. Whereas
efficient algorithms are known for computing the Fréchet distance of polygonal curves, the same problem for triangulated surfaces
is NP-hard. Furthermore, it remained open whether it is computable at all.
Using a discrete approximation, we show that it is upper semi-computable, i.e., there is a non-halting Turing machine which produces a decreasing sequence of rationals converging to the Fréchet
distance. It follows that the decision problem, whether the Fréchet distance of two given surfaces lies below a specified
value, is recursively enumerable. 相似文献
18.
In this paper, the semilocal convergence of a third order Stirling-like method used to find fixed points of nonlinear operator equations in Banach spaces is established under the assumption that the first Fréchet derivative of the involved operator satisfies ??-continuity condition. It turns out that this convergence condition is weaker than the Lipschitz and the H?lder continuity conditions on first Fréchet derivative of the involved operator. The importance of our work lies in the fact that numerical examples can be given to show that our approach is successful even in cases where Lipschitz and H?lder continuity conditions on first Fréchet derivative fail. It also avoids the evaluation of second order Fréchet derivative which is difficult to compute at times. A priori error bounds along with the domains of existence and uniqueness of a fixed point are derived. The R-order of the method is shown to be equal to (2p?+?1) for p????(0,1]. Finally, two numerical examples involving nonlinear integral equations are worked out to show the efficacy of our approach. 相似文献
19.
In this paper, in terms of the Fréchet normal cone, we establish exact separation results for finitely many disjoint closed sets in an Asplund space, which supplement the extremal principle and some fuzzy separation theorems. As an application, we provide a new optimality condition for a constraint optimization problem in terms of Fréchet subdifferential and Fréchet normal cone. 相似文献
20.
J. M. Borwein 《Israel Journal of Mathematics》1986,54(1):42-50
By studying partially monotone operators, we are able to show among other results that convex-concave and biconvex mappings
defined on Asplund spaces or dually strictly convex spaces are respectively generically Fréchet or Gateaux differentiable.
Research partially supported on a N.S.E.R.C. operating grant. 相似文献