Gap Functions and Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems

This paper deals with generalized vector quasi-equilibrium problems. By virtue of a nonlinear scalarization function, the gap functions for two classes of generalized vector quasi-equilibrium problems are obtained. Then, from an existence theorem for a generalized quasi-equilibrium problem and a minimax inequality, existence theorems for two classes of generalized vector quasi-equilibrium problems are established. This research is partially supported by the Postdoctoral Fellowship Scheme of The Hong Kong Polytechnic University and the National Natural Science Foundation of China.     

Decentralized Guaranteed Cost Control for Uncertain Large-Scale Systems Using Delayed Feedback: LMI Optimization Approach

In this paper, we propose a design method of guaranteed cost controllers for uncertain large-scale systems with time delays in subsystem interconnections using delayed feedback. Using the Lyapunov method, a linear matrix inequality (LMI) optimization problem is formulated to design a delayed feedback controller which minimizes the upper bound of a given quadratic cost function. A numerical example is included to illustrate the design procedures.Communicated by Q. C. ZhaoThe authors thank the Associate Editor and three anonymous referees for careful reading and useful suggestions.     

Validating DEA as a ranking tool: An application of DEA to assess performance in higher education

There is a general interest in ranking schemes applied to complex entities described by multiple attributes. Published rankings for universities are in great demand but are also highly controversial. We compare two classification and ranking schemes involving universities; one from a published report, ‘Top American Research Universities’ by the University of Florida's TheCenter and the other using DEA. Both approaches use the same data and model. We compare the two methods and discover important equivalences. We conclude that the critical aspect in classification and ranking is the model. This suggests that DEA is a suitable tool for these types of studies.     

Non-Parametric Regression Methods

The nature of the financial time series is complex, continuous interchange of stochastic and deterministic regimes. Therefore, it is difficult to forecast with parametric techniques. Instead of parametric models, we propose three techniques and compare with each other. Neural networks and support vector regression (SVR) are two universally approximators. They are data-driven non parametric models. ARCH/GARCH models are also investigated. Our assumption is that the future value of Istanbul Stock Exchange 100 index daily return depends on the financial indicators although there is no known parametric model to explain this relationship. This relationship comes from the technical analysis. Comparison shows that the multi layer perceptron networks overperform the SVR and time series model (GARCH).     

First and Second Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces

We use the first and second order approximations of mappings to establish both necessary and sufficient optimality conditions for unconstrained and constrained nonsmooth vector optimization problems. Ideal solutions, efficient solutions, and weakly efficient solutions are considered. The data of the problems need not even be continuous. Some often imposed compactness assumptions are also relaxed. Examples are provided to compare our results and some known recent results.This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam.     

Lower Bounds from State Space Relaxations for Concave Cost Network Flow Problems

In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are derived from state space relaxations of a dynamic programming formulation, which involve the use of non-injective mapping functions guaranteing a reduction on the cardinality of the state space. The general state space relaxation procedure is extended to address problems involving transitions that go across several stages, as is the case of network flow problems. Applications for these LBs include: estimation of the quality of heuristic solutions; local search methods that use information of the LB solution structure to find initial solutions to restart the search (Fontes et al., 2003, Networks, 41, 221–228); and branch-and-bound (BB) methods having as a bounding procedure a modified version of the LB algorithm developed here, (see Fontes et al., 2005a). These LBs are iteratively improved by penalizing, in a Lagrangian fashion, customers not exactly satisfied or by performing state space modifications. Both the penalties and the state space are updated by using the subgradient method. Additional constraints are developed to improve further the LBs by reducing the searchable space. The computational results provided show that very good bounds can be obtained for concave cost network flow problems, particularly for fixed-charge problems.     

η-Invariant and Flat Vector Bundles

Abstract We present an alternate definition of the mod Z component of the Atiyah-Patodi-Singer η invariant associated to (not necessary unitary) flat vector bundles, which identifies explicitly its real and imaginary parts. This is done by combining a deformation of flat connections introduced in a previous paper with the analytic continuation procedure appearing in the original article of Atiyah, Patodi and Singer. * Project supported by the Cheung-Kong Scholarship of the Ministry of Education of China and the 973 Project of the Ministry of Science and Technology of China. (Dedicated to the memory of Shiing-Shen Chern)     

A Constraint Programming Approach to Extract the Maximum Number of Non-Overlapping Test Forms

This paper introduces a novel approach for extracting the maximum number of non-overlapping test forms from a large collection of overlapping test sections assembled from a given item bank. The approach involves solving maximum set packing problems (MSPs). A branch-and-bound MSP algorithm is developed along with techniques adapted from constraint programming to estimate lower and upper bounds on the optimal MSP solution. The algorithm is general and can be applied in other applications including combinatorial auctions. The results of computer simulations and experiments with an operational item bank are presented. An erratum to this article is available at .     

Reductions of interval nonlinear programming problem

A general nonlinear programming problem with interval functions is considered. Two reductions of this problem to the deterministic nonlinear programming problem are proposed, and illustrative examples are discussed.     

Some Notes on the Linear Complexity of Sidel’nikov-Lempel-Cohn-Eastman Sequences

We continue the study of the linear complexity of binary sequences, independently introduced by Sidel’nikov and Lempel, Cohn, and Eastman. These investigations were originated by Helleseth and Yang and extended by Kyureghyan and Pott. We determine the exact linear complexity of several families of these sequences using well-known results on cyclotomic numbers. Moreover, we prove a general lower bound on the linear complexity profile for all of these sequences.