共查询到20条相似文献,搜索用时 46 毫秒
1.
In this paper, we employ the image space analysis (for short, ISA) to investigate vector quasi-equilibrium problems (for short, VQEPs) with a variable ordering relation, the constrained condition of which also consists of a variable ordering relation. The quasi relatively weak VQEP (for short, qr-weak VQEP) are defined by introducing the notion of the quasi relative interior. Linear separation for VQEP (res., qr-weak VQEP) is characterized by utilizing the quasi interior of a regularization of the image and the saddle points of generalized Lagrangian functions. Lagrangian type optimality conditions for VQEP (res., qr-weak VQEP) are then presented. Gap functions for VQEP (res., qr-weak VQEP) are also provided and moreover, it is shown that an error bound holds for the solution set of VQEP (res., qr-weak VQEP) with respect to the gap function under strong monotonicity. 相似文献
2.
We study the Clarke–Rockafellar directional derivatives of the regularized gap functions (and of some modified ones) for the
variational inequality problem (VIP) defined by a locally Lipschitz but not necessarily differentiable function on a closed
convex set in an Euclidean space. As applications we show that, under the strong monotonicity assumption, the regularized
gap functions have fractional exponent error bounds and consequently that the sequences provided by an algorithm of Armijo
type converge to the solution of the (VIP).
The research of this author was supported by an Earmarked Grant from the Research Council of Hong Kong. 相似文献
3.
J.-S. Chen 《Journal of Optimization Theory and Applications》2007,132(3):459-473
Recently this author studied several merit functions systematically for the second-order cone complementarity problem. These
merit functions were shown to enjoy some favorable properties, to provide error bounds under the condition of strong monotonicity,
and to have bounded level sets under the conditions of monotonicity as well as strict feasibility. In this paper, we weaken
the condition of strong monotonicity to the so-called uniform P
*-property, which is a new concept recently developed for linear and nonlinear transformations on Euclidean Jordan algebra.
Moreover, we replace the monotonicity and strict feasibility by the so-called R
01 or R
02-functions to keep the property of bounded level sets.
This work is partially supported by National Science Council of Taiwan. 相似文献
4.
Lu Lin Tan 《Journal of Mathematical Analysis and Applications》2007,334(2):1022-1038
Under the condition that the involved function F is locally Lipschitz, but not necessarily differentiable, we investigate the regularized gap function defined by a generalized distance function for the variational inequality problem (VIP). First, we compute exactly the Clarke-Rockafellar directional derivatives of the regularized gap functions (and of some modified ones). Second, using these results, we show that, under the strongly monotonicity assumption, the regularized gap functions have fractional exponent error bounds, and thereby we provide an algorithm of Armijo type to solve the VIP. 相似文献
5.
We study infinitesimal properties of nonsmooth (nondifferentiable) functions on smooth manifolds. The eigenvalue function of a matrix on the manifold of symmetric matrices gives a natural example of such a nonsmooth function.
A subdifferential calculus for lower semicontinuous functions is developed here for studying constrained optimization problems, nonclassical problems of calculus of variations, and generalized solutions of first-order partial differential equations on manifolds. We also establish criteria for monotonicity and invariance of functions and sets with respect to solutions of differential inclusions.
6.
7.
In this paper, characterizations of the set of solutions for VVI are presented by using scalarization approaches. The set of solutions of VVI is shown to be the set of weak sharpness for gap functions of some scalarization of VVI and for gap functions of VVI under semi-strong monotonicity. Some examples are given to illustrate these results. 相似文献
8.
In this paper, in order to obtain some existence results about solutions of the augmented Lagrangian problem for a constrained
problem in which the objective function and constraint functions are noncoercive, we construct a new augmented Lagrangian
function by using an auxiliary function. We establish a zero duality gap result and a sufficient condition of an exact penalization
representation for the constrained problem without the coercive or level-bounded assumption on the objective function and
constraint functions. By assuming that the sequence of multipliers is bounded, we obtain the existence of a global minimum
and an asymptotically minimizing sequence for the constrained optimization problem. 相似文献
9.
In this paper, the image space analysis is applied to investigate scalar-valued gap functions and their applications for a (parametric)-constrained vector variational inequality. Firstly, using a non-linear regular weak separation function in image space, a gap function of a constrained vector variational inequality is obtained without any assumptions. Then, as an application of the gap function, two error bounds for the constrained vector variational inequality are derived by means of the gap function under some mild assumptions. Further, a parametric gap function of a parametric constrained vector variational inequality is presented. As an application of the parametric gap function, a sufficient condition for the continuity of the solution map of the parametric constrained vector variational inequality is established within the continuity and strict convexity of the parametric gap function. These assumptions do not include any information on the solution set of the parametric constrained vector variational inequality. 相似文献
10.
In this paper, by using the scalarization approach of Konnov, several kinds of strong and weak scalar variational inequalities
(SVI and WVI) are introduced for studying strong and weak vector variational inequalities (SVVI and WVVI) with set-valued
mappings, and their gap functions are suggested. The equivalence among SVVI, WVVI, SVI, WVI is then established under suitable
conditions and the relations among their gap functions are analyzed. These results are finally applied to the error bounds
for gap functions. Some existence theorems of global error bounds for gap functions are obtained under strong monotonicity
and several characterizations of global (respectively local) error bounds for the gap functions are derived. 相似文献
11.
The generalized Marcum functions appear in problems of technical and scientific areas such as, for example, radar detection and communications. In mathematical statistics and probability theory these functions are called the noncentral gamma or the noncentral chi‐squared cumulative distribution functions. In this paper, we describe a new asymptotic method for inverting the generalized Marcum Q‐function and for the complementary Marcum P‐function. Also, we show how monotonicity and convexity properties of these functions can be used to find initial values for reliable Newton or secant methods to invert the function. We present details of numerical computations that show the reliability of the asymptotic approximations. 相似文献
12.
M. V. Dolgopolik 《Optimization》2017,66(10):1577-1622
In this article, we develop a general theory of exact parametric penalty functions for constrained optimization problems. The main advantage of the method of parametric penalty functions is the fact that a parametric penalty function can be both smooth and exact unlike the standard (i.e. non-parametric) exact penalty functions that are always nonsmooth. We obtain several necessary and/or sufficient conditions for the exactness of parametric penalty functions, and for the zero duality gap property to hold true for these functions. We also prove some convergence results for the method of parametric penalty functions, and derive necessary and sufficient conditions for a parametric penalty function to not have any stationary points outside the set of feasible points of the constrained optimization problem under consideration. In the second part of the paper, we apply the general theory of exact parametric penalty functions to a class of parametric penalty functions introduced by Huyer and Neumaier, and to smoothing approximations of nonsmooth exact penalty functions. The general approach adopted in this article allowed us to unify and significantly sharpen many existing results on parametric penalty functions. 相似文献
13.
Tong Xiaojiao Zhou Shuzi Dept. of Appl.Math. Hunan Univ. Changsha . Dept.of Math. Changsha Univ.of Electric Power Changsha 《高校应用数学学报(英文版)》2000,(2)
§ 1 IntroductionIn this paper we study the following nonlinear equality constrained optimization prob-lem:minimize f(x) ,subjectto h(x) =0 ,(P)where h(x) =(h1 (x) ,h2 (x) ,...,hm(x) ) T,f and hi(i=1 ,2 ,...,m) are Rn→R twice conti-nously differentiable(m≤n) .Many authors have studied the problem(P) with trustregion method(see,references[1~ 3 ] ) .These methods have the same property:to enforce strict monotonicity for meritfunction at every iteration.Paper[4 ] shows thatstrictmonotonic … 相似文献
14.
TongXiaojiao ZhouShuzi 《高校应用数学学报(英文版)》2000,15(2):201-210
Abstract. A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm is proved under the same conditions of usual trust regionmethod. 相似文献
15.
In this paper our aim is to show some new inequalities of the Redheffer type for Bessel and modified Bessel functions of the first kind. The key tools in our proofs are some classical results on the monotonicity of quotients of differentiable functions as well as on the monotonicity of quotients of two power series. We also use some known results on the quotients of Bessel and modified Bessel functions of the first kind, and by using the monotonicity of the Dirichlet eta function we prove a sharp inequality for the tangent function. At the end of the paper a conjecture is stated, which may be of interest for further research. 相似文献
16.
Utility function properties as monotonicity and concavity play a fundamental role in reflecting a decision-maker’s preference structure. These properties are usually characterized via partial derivatives. However, elicitation methods do not necessarily lead to twice-differentiable utility functions. Furthermore, while in a single-attribute context concavity fully reflects risk aversion, in multiattribute problems such correspondence is not one-to-one. We show that Tsetlin and Winkler’s multivariate risk attitudes imply ultramodularity of the utility function. We demonstrate that geometric properties of a multivariate utility function can be successfully studied by utilizing an integral function expansion (functional ANOVA). The necessary and sufficient conditions under which monotonicity and/or ultramodularity of single-attribute functions imply the monotonicity and/or ultramodularity of the corresponding multiattribute function under additive, preferential and mutual utility independence are then established without reliance on the utility function differentiability. We also investigate the relationship between the presence of interactions among the attributes of a multiattribute utility function and the decision-maker’s multivariate risk attitudes. 相似文献
17.
《Journal of computational and graphical statistics》2013,22(3):592-614
This article shows how to smoothly “monotonize” standard kernel estimators of hazard rate, using bootstrap weights. Our method takes a variety of forms, depending on choice of kernel estimator and on the distance function used to define a certain constrained optimization problem. We confine attention to a particularly simple kernel approach and explore a range of distance functions. It is straightforward to reduce “quadratic” inequality constraints to “linear” equality constraints, and so our method may be implemented using little more than conventional Newton–Raphson iteration. Thus, the necessary computational techniques are very familiar to statisticians. We show both numerically and theoretically that monotonicity, in either direction, can generally be imposed on a kernel hazard rate estimator regardless of the monotonicity or otherwise of the true hazard rate. The case of censored data is easily accommodated. Our methods have straightforward extension to the problem of testing for monotonicity of hazard rate, where the distance function plays the role of a test statistic. 相似文献
18.
We consider probabilistically constrained linear programs with general distributions for the uncertain parameters. These problems
involve non-convex feasible sets. We develop a branch-and-bound algorithm that searches for a global optimal solution to this
problem by successively partitioning the non-convex feasible region and by using bounds on the objective function to fathom
inferior partition elements. This basic algorithm is enhanced by domain reduction and cutting plane strategies to reduce the
size of the partition elements and hence tighten bounds. The proposed branch-reduce-cut algorithm exploits the monotonicity properties inherent in the problem, and requires solving linear programming subproblems.
We provide convergence proofs for the algorithm. Some illustrative numerical results involving problems with discrete distributions
are presented. 相似文献
19.
Admissible slopes for monotone and convex interpolation 总被引:1,自引:0,他引:1
Summary In many applications, interpolation of experimental data exhibiting some geometric property such as nonnegativity, monotonicity or convexity is unacceptable unless the interpolant reflects these characteristics. This paper identifies admissible slopes at data points of variousC
1 interpolants which ensure a desirable shape. We discuss this question, in turn for the following function classes commonly used for shape preserving interpolations: monotone polynomials,C
1 monotone piecewise polynomials, convex polynomials, parametric cubic curves and rational functions. 相似文献
20.
Houyuan Jiang 《Journal of Global Optimization》1996,9(2):169-181
The nonlinear complementarity problem can be reformulated as unconstrained minimization problems by introducing merit functions. Under some assumptions, the solution set of the nonlinear complementarity problem coincides with the set of local minima of the corresponding minimization problem. These results were presented by Mangasarian and Solodov, Yamashita and Fukushima, and Geiger and Kanzow. In this note, we generalize some results of Mangasarian and Solodov, Yamashita and Fukushima, and Geiger and Kanzow to the case where the considered function is only directionally differentiable. Some results are strengthened in the smooth case. For example, it is shown that the strong monotonicity condition can be replaced by the P-uniform property for ensuring a stationary point of the reformulated unconstrained minimization problems to be a solution of the nonlinear complementarity problem. We also present a descent algorithm for solving the nonlinear complementarity problem in the smooth case. Any accumulation point generated by this algorithm is proved to be a solution of the nonlinear complementarity under the monotonicity condition. 相似文献