Error bounds for convex differentiable inequality systems in Banach spaces

The paper is devoted to studying the Hoffman global error bound for convex quadratic/affine inequality/equality systems in the context of Banach spaces. We prove that the global error bound holds if the Hoffman local error bound is satisfied for each subsystem at some point of the solution set of the system under consideration. This result is applied to establishing the equivalence between the Hoffman error bound and the Abadie qualification condition, as well as a general version of Wang &; Pang's result [30], on error bound of Hölderian type. The results in the present paper generalize and unify recent works by Luo &; Luo in [17], Li in [16] and Wang &; Pang in [30].     

Enhanced Formaldehyde‐Vapor Adsorption Capacity of Polymeric Amine‐Incorporated Aminosilicas

Airborne formaldehyde, which is a highly problematic volatile organic compound (VOC) pollutant, is adsorbed by polymeric amine‐incorporated silicas (aminosilicas), and the factors that affect the adsorption performance are systematically investigated. Three different types of polymeric amines 1) poly(ethyleneimine) branched (PEIBR); 2) poly(ethyleneimine) linear (PEILI); and 3) poly(allylamine) (PAA) are impregnated into two types of porous silicas [SBA‐15 and mesocellular foam (MCF) silicas] with systematic changes of the amine loadings. The adsorption results demonstrate that the adsorption capacity increases along with the amine loading until the polymeric amines completely fill the silica pores. This results in the MCF silica, which has a larger pore volume and hence can accommodate more polymeric amine before completely filling the pore, giving materials that adsorb more formaldehyde, with the largest adsorption capacity, q, of up to 5.7 mmol_HCHO g^?1 among the samples studied herein. Of the three different types of polymers, PAA, comprised of 100 % primary amines, showed the highest amine efficiency μ (mmol_HCHO/mmol_N) for capturing formaldehyde. The chemical structures of the adsorbed formaldehyde are analyzed by ¹³C cross‐polarization magic‐angle spinning (CP‐MAS) NMR, and it is demonstrated that the adsorbed formaldehyde is chemically attached to the aminosilica surface, forming hemiaminal and imine species. Because the chemical adsorption of formaldehyde forms covalent bonds, it is not desorbed from the aminosilicas below 130 °C based on temperature‐programed‐desorption (TPD) analysis. The high formaldehyde‐adsorption capacity and stability of the trapped formaldehyde on the amine surface in this study reveal the potential utility of aminosilicas as formaldehyde abatement materials.     

One-Parameter Families of Feasible Sets in Semi-infinite Optimization

Feasible sets in semi-infinite optimization are basically defined by means of infinitely many inequality constraints. We consider one-parameter families of such sets. In particular, all defin-ing functions - including those defining the index set of the inequality constraints - will depend on a parameter. We note that a semi-infinite problem is a two-level problem in the sense that a point is feasible if and only if all global minimizers of a corresponding marginal function are nonnegative. For a quite natural class of mappings we characterize changes in the global topological structure of the corresponding feasible set as the parameter varies. As long as the index set (-mapping) of the inequality constraints is lower semicontinuous, all changes in topology are those which generically appear in one-parameter sets defined by finitely many constraints. In the case, however, that some component of the mentioned index set is born (or vanishes), the topological change is of global nature and is not controllable. In fact, the change might be as drastic as that when adding or deleting an (arbitrary) inequality constraint.     

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.     

Modified relaxation method for mathematical programs with complementarity constraints

In this paper, we suggest a new relaxation method for solving mathematical programs with complementarity constraints. This method can be regarded as a modification of a method proposed in a recent paper (J. Opt. Theory Appl. 2003; 118 :81–116). We show that the main results remain true for the modified method and particularly, some conditions assumed in the previous paper can be removed. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Pairs of monotone operators

This note is an addendum to Sum theorems for monotone operators and convex functions. In it, we prove some new results on convex functions and monotone operators, and use them to show that several of the constraint qualifications considered in the preceding paper are, in fact, equivalent.