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Abstract: In this paper, we suggest and analyze a new inexact proximal point method for solving general variational inequalities, which can be considered as an implicit predictor–corrector method. An easily measurable error term is proposed with further relaxed error bound and an optimal step length is obtained by maximizing the profit-function and is dependent on the previous points. Our results include several known and new techniques for solving variational inequalities and related optimization problems. Results obtained in this paper can be viewed as an important improvement and refinement of the previously known results. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: Design of an optimal shock-damping isolator is presented in this paper with specific application to casters. The design is first formulated as an optimization problem to minimize the peak acceleration of a load while keeping the maximal deflection of the isolator within a specified physical limit. The resulting solution is a constant force isolator. However, it is difficult to realize a constant force isolator with conventional mechanisms using linear springs and dampers. To implement such an isolator physically, a novel mechanism employing multiple linear springs has been developed. The structure and the parameters of the springs have been chosen by optimization techniques, and the resulting mechanism has been embodied in a prototype caster design. This paper presents the concept, design procedure, simulation and experimental evaluation results of a prototype optimal shock-damping caster in detail. The peak acceleration of this new design is only 65% of the existing caster. From a manufacturing point of view, this newly designed caster is not much more complex than existing ones. [Copyright &y& Elsevier]

A number of recent papers on approximation algorithms have used the square roots of unity, −1 and 1, to represent binary decision variables for problems in combinatorial optimization, and have relaxed these to unit vectors in real space using semidefinite programming in order to obtain near optimum solutions to these problems. In this paper, we consider using the cube roots of unity, 1, ei2π/3, and ei4π/3, to represent ternary decision variables for problems in combinatorial optimization. Here the natural relaxation is that of unit vectors in complex space. We use an extension of semidefinite programming to complex space to solve the natural relaxation, and use a natural extension of the random hyperplane technique introduced by the authors in Goemans and Williamson (J. ACM 42 (1995) 1115–1145) to obtain near-optimum solutions to the problems. In particular, we consider the problem of maximizing the total weight of satisfied equations xu−xv≡c (mod 3) and inequations xu−xv≢c (mod 3), where xu∈{0,1,2} for all u. This problem can be used to model the Max-3-Cut problem and a directed variant we call Max-3-Dicut. For the general problem, we obtain a 0.793733-approximation algorithm. If the instance contains only inequations (as it does for Max-3-Cut), we obtain a performance guarantee of 7/12+3/4π2arccos2(−1/4)−ϵ>0.836008. This compares with proven performance guarantees of 0.800217 for Max-3-Cut (by Frieze and Jerrum (Algorithmica 18 (1997) 67–81) and 1/3+3/4π2arccos2(−1/4)−ϵ>0.836008. This compares with proven performance guarantees of 0.800217 for Max-3-Cut (by Frieze and Jerrum (Algorithmica 18 (1997) 67–81) and 1/3 arccos2(−1/4)−ϵ>0.836008. This compares with proven performance guarantees of 0.800217 for Max-3-Cut (by Frieze and Jerrum (Algorithmica 18 (1997) 67–81) and 1/3+10−8 for the general problem (by Andersson et al. (J. Algorithms 39 (2001) 162–204)). It matches the guarantee of 0.836008 for Max-3-Cut found independently by de Klerk et al. (On approximate graph colouring and Max-k-Cut algorithms based on the ϑ-function, Manuscript, October 2000). We show that all these algorithms are in fact equivalent in the case of Max-3-Cut, and that our algorithm is the same as that of Andersson et al. in the more general case. [Copyright &y& Elsevier]

The paper considers the problem of updating an analytical model from experimental data using the reference basis approach. In the general framework of the reference basis method, certain quantities, e.g., natural frequencies or modeshapes, are considered to be completely accurate and the others are updated by solving a constrained optimization problem. However, the underlying structure, known as connectivity, existing in the model is not preserved, and the method is not suited for parametric updating. In this paper, a method for introducing connectivity constraints into reference basis, while maintaining its advantages, is presented. It brings the reference basis method closer to a broad class of updating methods that use parametric updating. The notions of “connectivity cost” and “parameterization cost” are defined and used to obtain the best model for a given parameterization and to compare the outcomes of different parameterizations. [Copyright &y& Elsevier]

Abstract: In this paper we present a new primal-dual path-following interior-point algorithm for semidefinite optimization. The algorithm is based on a new technique for finding the search direction and the strategy of the central path. At each iteration, we use only full Nesterov–Todd step. Moreover, we obtain the currently best known iteration bound for the algorithm with small-update method, namely, , which is as good as the linear analogue. [Copyright &y& Elsevier]

Abstract: Factorial designs are arguably the most widely used designs in scientific investigations. Generalized minimum aberration (GMA) and uniformity are two important criteria for evaluating both regular and non-regular designs. The generation of GMA designs is a non-trivial problem due to the sequential optimization nature of the criterion. Based on an analytical expression between the generalized wordlength pattern and a uniformity measure, this paper converts the generation of GMA designs to a constrained optimization problem, and provides effective algorithms for solving this particular problem. Moreover, many new designs with GMA or near-GMA are reported, which are also (nearly) optimal under the uniformity measure. [Copyright &y& Elsevier]

Abstract: In this paper, two conjugate dual problems based on weak efficiency to a constrained vector optimization problem are introduced. Some inclusion relations between the dual objective mappings and the properties of the Lagrangian maps and their saddle points for primal problem are discussed. Gap functions for a vector equilibrium problem are established by using the weak and strong duality. [Copyright &y& Elsevier]

Abstract: In this paper, we establish the global estimates for divergence form elliptic equations in the Orlicz space , where Ω is a bounded Reifenberg domain in . Our result generalizes the estimates. [Copyright &y& Elsevier]

Abstract: The performance of an acoustic absorbent lining can be significantly enhanced by introducing holes inside the lining. Its performance is dependent on the material properties, thickness of layers as well as the size and distribution of holes. In this paper, a simulation-based design approach that combines the acoustic finite element method (FEM) and acoustic duct method (ADM) with a multi-variable optimization technique is proposed for the design synthesis of the acoustic absorbent lining. The proposed method treats a single cell of a periodic acoustic absorbent lining in isolation. The cell may contain a set of holes. Two acoustic ducts are attached at opposing faces of the isolated cell. FEM model is built for the cell and these two acoustic ducts. The reflection and transmission characteristics of acoustic absorbent lining are calculated simultaneously using the acoustic duct theory. The zero-order optimization method is applied to optimize the various design variables, such as Young''s modulus of the material, damping loss factors and the diameters of cylindrical holes, etc., to achieve the desirable acoustic performance of the absorbent lining at a single frequency of interest. The proposed method is validated against analytical solutions for a homogeneous acoustic absorbent lining. Numerical examples for the linings with different optimized results are presented to demonstrate the performance of the optimized absorbent lining. [Copyright &y& Elsevier]

Abstract: In this paper, we establish some relationships between vector variational-like inequality and vector optimization problems under the assumptions of α-invex functions. We identify the vector critical points, the weakly efficient points and the solutions of the weak vector variational-like inequality problems, under pseudo-α-invexity assumptions. These conditions are more general than those of existing ones in the literature. In particular, this work extends the earlier work of Ruiz-Garzon et al. [G. Ruiz-Garzon, R. Osuna-Gomez, A. Rufian-Lizan, Relationships between vector variational-like inequality and optimization problems, European J. Oper. Res. 157 (2004) 113–119] to a wider class of functions, namely the pseudo-α-invex functions studied in a recent work of Noor [M.A. Noor, On generalized preinvex functions and monotonicities, J. Inequal. Pure Appl. Math. 5 (2004) 1–9]. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a class of infinitely repeated games with imperfect public monitoring. We look at strongly symmetric perfect public equilibria with memory K: equilibria in which strategies are restricted to depend only on the last K observations of public signals. Define to be the set of payoffs of equilibria with memory K. We show that for some parameter settings, for sufficiently large K. However, for other parameter settings, we show that not only is , but that is a singleton. Moreover, this last result is essentially independent of the discount factor. [Copyright &y& Elsevier]

Abstract: In this paper, we extend the classes of generalized type I vector-valued functions introduced by Aghezzaf and Hachimi in [J. Global Optim. 18 (2000) 91–101] to generalized univex type I vector-valued functions and consider a multiple-objective optimization problem involving generalized type I univex functions. A number of Kuhn–Tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution. The Mond–Weir and general Mond–Weir type duality results are also presented. [Copyright &y& Elsevier]

In this paper we present first and second order sufficient conditions for strict local minima of orders 1 and 2 to vector optimization problems with an arbitrary feasible set and a twice directionally differentiable objective function. With this aim, the notion of support function to a vector problem is introduced, in such a way that the scalar case and the multiobjective case, in particular, are contained. The obtained results extend the multiobjective ones to this case. Moreover, specializing to a feasible set defined by equality, inequality, and set constraints, first and second order sufficient conditions by means of Lagrange multiplier rules are established. [Copyright &y& Elsevier]

Pipelined operator tree (POT) scheduling is an important problem in the area of parallel query optimization. A POT is a tree with nodes representing query operators that can run in parallel and edges representing communication between adjacent operators that is handled by sending long streams of data in a parallel-pipelined fashion. The problem is to find a schedule for the POT that minimizes the total response time. This problem has only been previously addressed for homogeneous environments, but the new parallel database systems tend to be more heterogeneous. In this paper, we consider processors with different fixed speeds (called uniform processor system). This problem has been shown to be NP-hard even for identical processors. We propose three approximate algorithms for some special cases of the problem with good low-performance ratio (or approximation factor) bound in the worst case. The performance ratios of these algorithms, even for the general case, are shown by experimentation to be near optimal on the average. We will show that the performance ratios of these algorithms, if used for homogeneous systems, are lower than the previous results. For the general case, we propose an algorithm which has a constant bound on the performance ratio in the worst case and is near optimal on the average. [Copyright &y& Elsevier]