共查询到20条相似文献,搜索用时 31 毫秒
1.
S. Abramovich 《Journal of Mathematical Analysis and Applications》2007,327(2):1444-1460
The concept of superquadratic functions in several variables, as a generalization of the same concept in one variable is introduced. Analogous results to results obtained for convex functions in one and several variables are presented. These include refinements of Jensen's inequality and its counterpart, and of Slater-Pe?ari?'s inequality. 相似文献
2.
We present some Farkas-type results for inequality systems involving finitely many DC functions. To this end we use the so-called
Fenchel-Lagrange duality approach applied to an optimization problem with DC objective function and DC inequality constraints.
Some recently obtained Farkas-type results are rediscovered as special cases of our main result. 相似文献
3.
In this paper we provide a duality theory for multiobjective optimization problems with convex objective functions and finitely many D.C. constraints. In order to do this, we study first the duality for a scalar convex optimization problem with inequality constraints defined by extended real-valued convex functions. For a family of multiobjective problems associated to the initial one we determine then, by means of the scalar duality results, their multiobjective dual problems. Finally, we consider as a special case the duality for the convex multiobjective optimization problem with convex constraints. 相似文献
4.
We present an extension of Fenchel’s duality theorem by weakening the convexity assumptions to near convexity. These weak
hypotheses are automatically fulfilled in the convex case. Moreover, we show by a counterexample that a further extension
to closely convex functions is not possible under these hypotheses.
The authors are grateful to the Associate Editor for helpful suggestions and remarks which improved the quality of the paper.
The second author was supported by DFG (German Research Foundation), project WA 922/1. 相似文献
5.
We deal with duality for almost convex finite dimensional optimization problems by means of the classical perturbation approach.
To this aim some standard results from the convex analysis are extended to the case of almost convex sets and functions. The
duality for some classes of primal-dual problems is derived as a special case of the general approach. The sufficient regularity
conditions we need for guaranteeing strong duality are proved to be similar to the ones in the convex case.
The research of the first and third authors was partially supported by DFG (German Research Foundation), project WA 922/1.
The research of the second author was supported by the grant PN II, ID 523/2007. 相似文献
6.
指数凸函数的积分不等式及其在Gamma函数中的应用 总被引:1,自引:0,他引:1
何晓红 《纯粹数学与应用数学》2014,(1):69-76
仿对数凸函数的概念,给出指数凸函数的定义,并证明有关指数凸函数的几个积分不等式,作为应用,得到一个新的Kershaw型双向不等式. 相似文献
7.
X.Q. Yang 《Journal of Optimization Theory and Applications》2003,116(2):437-452
Gap functions play a crucial role in transforming a variational inequality problem into an optimization problem. Then, methods solving an optimization problem can be exploited for finding a solution of a variational inequality problem. It is known that the so-called prevariational inequality is closely related to some generalized convex functions, such as linear fractional functions. In this paper, gap functions for several kinds of prevariational inequalities are investigated. More specifically, prevariational inequalities, extended prevariational inequalities, and extended weak vector prevariational inequalities are considered. Furthermore, a class of gap functions for inequality constrained prevariational inequalities is investigated via a nonlinear Lagrangian. 相似文献
8.
In this paper we work in separated locally convex spaces where we give equivalent statements for the formulae of the conjugate function of the sum of a convex lower‐semicontinuous function and the precomposition of another convex lower‐semicontinuous function which is also K ‐increasing with a K ‐convex K ‐epi‐closed function, where K is a nonempty closed convex cone. These statements prove to be the weakest constraint qualifications given so far under which the formulae for the subdifferential of the mentioned sum of functions are valid. Then we deliver constraint qualifications inspired from them that guarantee some conjugate duality assertions. Two interesting special cases taken from the literature conclude the paper. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
9.
Craig A. Nolder 《Journal of Mathematical Analysis and Applications》2005,302(1):137-142
We generalize a Hardy-Littlewood inequality and a Privalov inequality for conjugate harmonic functions in the plane to components of Clifford-valued monogenic functions. 相似文献
10.
关于几何凸函数的Hadamard型不等式 总被引:7,自引:1,他引:6
张小明 《数学的实践与认识》2004,34(9):171-176
建立了一个关于几何凸函数的 Hadamard型不等式 . 相似文献
11.
Sien Deng 《Mathematical Programming》1998,83(1-3):263-276
In this paper several types of perturbations on a convex inequality system are considered, and conditions are obtained for
the system to be well-conditioned under these types of perturbations, where the well-conditionedness of a convex inequality
system is defined in terms of the uniform boundedness of condition numbers under a set of perturbations. It is shown that
certain types of perturbations can be used to characterize the well-conditionedness of a convex inequality system, in which
either the system has a bounded solution set and satisfies the Slater condition or an associated convex inequality system,
which defines the recession cone of the solution set for the system, satisfies the Slater condition. Finally, sufficient conditions
are given for the existence of a global error bound for an analytic system. It is shown that such a global error bound always
holds for any inequality system defined by finitely many convex analytic functions when the zero vector is in the relative
interior of the domain of an associated convex conjugate function. 相似文献
12.
《Mathematische Nachrichten》2018,291(10):1502-1513
We obtain sharp estimates for a generalized Zalcman coefficient functional with a complex parameter for the Hurwitz class and the Noshiro–Warschawski class of univalent functions as well as for the closed convex hulls of the convex and starlike functions by using an inequality from [6]. In particular, we generalize an inequality proved by Ma for starlike functions and answer a question from his paper [17]. Finally, we prove an asymptotic version of the generalized Zalcman conjecture for univalent functions and discuss various related or equivalent statements which may shed further light on the problem. 相似文献
13.
P. Tseng 《Journal of Optimization Theory and Applications》1995,85(2):489-494
Recently, Fang proposed approximating a linear program in Karmarkar's standard form by adding an entropic barrier function to the objective function and using a certain geometric inequality to transform the resulting problem into an unconstrained differentiable concave program. We show that, by using standard duality theory for convex programming, the results of Fang and his coworkers can be strengthened and extended to linearly constrained convex programs and more general barrier functions.This research was supported by the National Science Foundation, Grant No. CCR-91-03804. 相似文献
14.
Hannelore Lisei Andrea Éva Molnár 《Journal of Mathematical Analysis and Applications》2011,378(2):741-748
In this paper we prove the existence of at least one solution for a variational-hemivariational inequality on a closed and convex set without using critical point theory. We apply a version of the well-known theorem of Knaster-Kuratowski-Mazurkiewicz. The obtained results can be applied to Schrödinger type problems and to problems with radially symmetric functions. 相似文献
15.
Shahid Khan Muhammad Adil Khan Yu-Ming Chu 《Mathematical Methods in the Applied Sciences》2020,43(5):2577-2587
Jensen integral inequality has got much importance regarding their applications in different fields of mathematics. In this paper, two converses of Jensen integral inequality for convex function are obtained. The results are applied to establish converses of Hölder and Hermite-Hadamard inequalities as well. At the end, some useful applications in information theory of the obtained results are given. The idea used in this paper may inculcate further research. 相似文献
16.
Let $I$ be an open interval of $\mathbb{R}$ and $f: I\to \mathbb{R}$. It is well-known that $f$ is convex in $I$ if and only if, for all $x,y\in I$ with $x相似文献
17.
Conjugate function theory is used to develop dual programs for nonseparable convex programs involving the square root function.
This function arises naturally in finance when one measures the risk of a portfolio by its variance–covariance matrix, in
stochastic programming under chance constraints and in location theory. 相似文献
18.
Radu Ioan Boţ Ioan Bogdan Hodrea Gert Wanka 《Central European Journal of Mathematics》2008,6(3):453-468
We consider a convex optimization problem with a vector valued function as objective function and convex cone inequality constraints.
We suppose that each entry of the objective function is the composition of some convex functions. Our aim is to provide necessary
and sufficient conditions for the weakly efficient solutions of this vector problem. Moreover, a multiobjective dual treatment
is given and weak and strong duality assertions are proved.
相似文献
19.
20.
Radu Ioan Bo? Sorin-Mihai Grad 《Journal of Mathematical Analysis and Applications》2008,337(2):1315-1325
We give some necessary and sufficient conditions which completely characterize the strong and total Lagrange duality, respectively, for convex optimization problems in separated locally convex spaces. We also prove similar statements for the problems obtained by perturbing the objective functions of the primal problems by arbitrary linear functionals. In the particular case when we deal with convex optimization problems having infinitely many convex inequalities as constraints the conditions we work with turn into the so-called Farkas-Minkowski and locally Farkas-Minkowski conditions for systems of convex inequalities, recently used in the literature. Moreover, we show that our new results extend some existing ones in the literature. 相似文献