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1.
Benson Proper Efficiency in the Vector Optimization of Set-Valued Maps   总被引:34,自引:0,他引:34  
This paper extends the concept of cone subconvexlikeness of single-valued maps to set-valued maps and presents several equivalent characterizations and an alternative theorem for cone-subconvexlike set-valued maps. The concept and results are then applied to study the Benson proper efficiency for a vector optimization problem with set-valued maps in topological vector spaces. Two scalarization theorems and two Lagrange multiplier theorems are established. After introducing the new concept of proper saddle point for an appropriate set-valued Lagrange map, we use it to characterize the Benson proper efficiency. Lagrange duality theorems are also obtained  相似文献
2.
Lagrange Multipliers and saddle points in multiobjective programming   总被引:4,自引:0,他引:4  
In this paper, we present several conditions for the existence of a Lagrange multiplier or a weak saddle point in multiobjective optimization. Relations between a Lagrange multiplier and a weak saddle point are established. A sufficient condition is also given for the equivalence of the Benson proper efficiency and the Borwein proper efficiency.This research was supported by NSFC under Grant No. 78900011 and by BMADIS. The authors are grateful to two referees for supplying valuable comments and pointing out detailed corrections to the draft paper. The authors also wish to thank Dr. P. L. Yu for valuable comments and suggestions.The revised version of this paper was completed while the second author visited the Faculty of Technical Mathematics and Informatics, Delft University of Technology, Delft, The Netherlands.  相似文献
3.
Risk-sensitive dynamic pricing for a single perishable product   总被引:1,自引:0,他引:1  
We show that the monotone structures of dynamic pricing for a single perishable product under risk-neutrality are preserved under risk-sensitivity with the additive general utility and atemporal exponential utility functions. We also show that the optimal price is decreasing over the degree of risk-sensitivity under the exponential class of both additive and atemporal utility functions.  相似文献
4.
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
5.
The paper discusses the stability of suitably-defined maxima of a set of i.i.d. random variables with multidimensional indices.It is shown that theorems of Gnedenko (1943) and Tomkins (1986) concerning relative stability and complete relative stability of maxima remain valid in the new setting.Moreover, a criterion for almost sure relative stability for maxima with multidimensional indices is presented, extending a result of Barndorff-Nielsen (1963).AMS 2000 Subject Classification. Primary—60F15, 60G60, 62G30, Secondary—10A25, 60G99  相似文献
6.
This paper is concerned with the implementation and testing of an algorithm for solving constrained least-squares problems. The algorithm is an adaptation to the least-squares case of sequential quadratic programming (SQP) trust-region methods for solving general constrained optimization problems. At each iteration, our local quadratic subproblem includes the use of the Gauss–Newton approximation but also encompasses a structured secant approximation along with tests of when to use this approximation. This method has been tested on a selection of standard problems. The results indicate that, for least-squares problems, the approach taken here is a viable alternative to standard general optimization methods such as the Byrd–Omojokun trust-region method and the Powell damped BFGS line search method.  相似文献
7.
Fix an integerr1. For eachnr, letM nr be the rth largest ofX 1,...,X n, where {X n,n1} is a sequence of i.i.d. random variables. Necessary and sufficient conditions are given for the convergence of n=r n P[|M nr /a n –1|<] for every >0, where {a n} is a real sequence and –1. Moreover, it is shown that if this series converges for somer1 and some >–1, then it converges for everyr1 and every >–1.  相似文献
8.
We study casino revenue management through the pricing of hotel rooms in the presence of gaming revenue, which is random. We identify a stochastic order based on customers’ gaming profiles, from which a monotonic inventory price of rooms is obtained. We develop a threshold-type pricing policy for a special customer segmentation scheme that allows customers’ winning profiles to be ranked in terms of the failure rate order. Our results shed new light on customer valuation and market segmentation.  相似文献
9.
This paper provides a unified framework to study monotone optimal control for a class of Markov decision processes through D-multimodularity. We demonstrate that each system in this class can be classified as either a substitution-type or a complement-type system according to the possible transition set, which can be used as a classification mechanism that integrates a variety of models in the literature. We develop a generic proof of the structural properties of both types of system. In particular, we show that D-multimodularity is a generally sufficient condition for monotone optimal control of different types of system in this class. With this unified theory, there is no need to pursue each problem ad hoc and the structural properties of this class of MDPs follow with ease.  相似文献
10.
This paper introduces the multimodularity concept to study structural properties for certain class of stochastic dynamic control problems through a new efficient approach. We demonstrate that this approach can substantially simplify the proofs of the main results of one recent article and provide an alternative method for two other models in the literature.  相似文献
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