关于结构KKT方程组的扰动分析

We discuss the perturbation analysis for the structured KKT systems. The methods and results of forward perturbation analysis all differ from the recent works of Gulliksson and other authors. The optimal backward perturbation results can not be deduced by the corresponding results of Sun about the KKT systems.     

Obtaining an outer approximation of the efficient set of nonlinear biobjective problems

A new method for obtaining an outer approximation of the efficient set of nonlinear biobjective optimization problems is presented. It is based on the well known ‘constraint method’, and obtains a superset of the efficient set by computing the regions of δ-optimality of a finite number of single objective constraint problems. An actual implementation, which makes use of interval tools, shows the applicability of the method and the computational studies on a set of competitive location problems demonstrate its efficiency. An extended version of this paper, with more comments, details, examples, and references, can be found in Fernández and Tóth [5]. This paper has been supported by the Ministry of Education and Science of Spain under the research project SEJ2005-06273/ECON, in part financed by the European Regional Development Fund (ERDF). Boglárka Tóth—On leave from the Research Group on Artificial Intelligence of the Hungarian Academy of Sciences and the University of Szeged, H-6720 Szeged, Aradi vértanúk tere 1., Hungary.     

Decision-support with preference constraints

One approach to Human Centered Processing is to take into account preferences of users within the context of multiple criteria optimization. The preference model of a problem encloses all the information needed to evaluate the quality of solutions.     

New Results on Second-Order Optimality Conditions in Vector Optimization Problems

In this paper, we study second-order optimality conditions for multiobjective optimization problems. By means of different second-order tangent sets, various new second-order necessary optimality conditions are obtained in both scalar and vector optimization. As special cases, we obtain several results found in the literature (see reference list). We present also second-order sufficient optimality conditions so that there is only a very small gap with the necessary optimality conditions. The authors thank Professor P.L. Yu and the referees for valuable comments and helpful suggestions.     

Digraph matrix partitions and trigraph homomorphisms

Matrix partitions generalize graph colourings and homomorphisms. Their study has so far been confined to symmetric matrices and undirected graphs. In this paper we make an initial study of list matrix partitions for digraphs; in other words our matrices are not necessarily symmetric. We motivate future conjectures by classifying the complexity of all list matrix partition problems for matrices of size up to three. We find it convenient to model the problem in the language of trigraph homomorphisms.     

Array signal processing with two outputs preserving binaural information

A new type of array signal processing combined with a weighted least squares algorithm to enable two-channel output with binaural information is proposed in this paper. This algorithm may be effective for use in a binaural hearing aid because the interaural relationship can be preserved after array signal processing. Retaining spatial information on specified directions while sufficiently suppressing unnecessary ambient noise coming from directions other than those of target sounds is required for this type of algorithm. In order to satisfy these two simultaneous requirements, the proposed algorithm was derived from a constraint algorithm by employing the weighted least squares algorithm. Performance in directivity patterns as well as interaural time difference (ITD) and interaural level difference (ILD) were evaluated. Computer simulations showed that this algorithm yields robust performance in various conditions compared with array signal processing based on a constraint algorithm.     

带梯度障碍的抛物型变分不等式解的存在性唯一性和正则性

本文讨论带梯度障碍的抛物型变分不等式解的存在性、唯一性和正则性问题．通过证明一类带梯度障碍的问题的求解等价于解某个双边障碍的问题，并利用双边障碍问题解的存在性、唯一性和正则性，得到了带梯度障碍的问题的相应结果．这一方法将有助于对具有梯度约束的非线性以及完全非线性抛物型方程解的正则性的研究．     

A Constraint Satisfaction Approach to a Circuit Design Problem

A classical circuit-design problem from Ebers and Moll (1954) features a system of nine nonlinear equations in nine variables that is very challenging both for local and global methods. This system was solved globally using an interval method by Ratschek and Rokne (1993) in the box [0, 10]⁹. Their algorithm had enormous costs (i.e., over 14 months using a network of 30 Sun Sparc-1 workstations) but they state that ‘at this time, we know no other method which has been applied to this circuit design problem and which has led to the same guaranteed result of locating exactly one solution in this huge domain, completed with a reliable error estimate’. The present paper gives a novel branch-and-prune algorithm that obtains a unique safe box for the above system within reasonable computation times. The algorithm combines traditional interval techniques with an adaptation of discrete constraint-satisfaction techniques to continuous problems. Of particular interest is the simplicity of the approach. This revised version was published online in July 2006 with corrections to the Cover Date.     

A projected semismooth Newton method for problems of calibrating least squares covariance matrix

In this paper we propose a projected semismooth Newton method to solve the problem of calibrating least squares covariance matrix with equality and inequality constraints. The method is globally and quadratically convergent with proper assumptions. The numerical results show that the proposed method is efficient and comparable with existing methods.     

Optimality conditions and the basic constraint qualification for quasiconvex programming

In this paper, we consider optimality conditions and a constraint qualification for quasiconvex programming. For this purpose, we introduce a generator and a new subdifferential for quasiconvex functions by using Penot and Volle’s theorem.