A CLASS OF REVISED BROYDEN ALGORITHMS

In this paper, we discuss the convergence of the Broyden algorithms with revised search direction. Under some inexact llne searches, we prove that the algorithms are globally convergent for continuously differentiable functions and the rate of convergence of the algorithms is one-step superlinear and n-step second-order for uniformly convex objective functions.     

Solvability of vector Ky Fan inequalities with applications

This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets. For vector-valued functions with the cone semicontinuity and the cone quasicon- vexity in infinite dimensional spaces, the authors prove some existence results of the solutions and the compactness of the solution sets. Especially, some results for the vector Ky Fan inequalities on noncompact sets are built and the compactness of its solution sets are also discussed. As applications, some existence theorems of the solutions of vector variational inequalities are obtained.     

New Results on H_∞ Control of Linear Systems with Interval Time-Varying Delays

This paper is focused on the H_(∞) control problem for linear systems with interval timevarying delays.By employing a reciprocally convex combination approach and a delay decomposition approach,some new delay-dependent bounded real lemmas(BRLs) are derived such that the closedloop system is asymptotically stable with a prescribed H_(∞) level.The BRLs are then used to solve the H_(∞) controller design by incorporating with the cone complementary approach.Three numerical examples are finally given to show the validity of the proposed method.     

Cooperative games on convex geometries with a coalition structure

This paper is mainly to discuss cooperative games on convex geometries with a coalition structure,which can be seen as an extension of cooperative games with a coalition structure.For this kind of games,the cooperation among unions and within each union will be the convex sets,i.e., the feasible subsets of the coalition structure and that of each union belong to a convex geometry, respectively.The explicit form of the generalized Owen value for this kind of games is given,which can be seen as an extension of the Owen value.Furthermore,two special cases of this kind of games are researched.The corresponding payoff indices are also studied.Finally,an illustrative example is given.     

ROLE OF α-PSEUDO-UNIVEX FUNCTIONS IN VECTOR VARIATIONAL-LIKE INEQUALITY PROBLEMS

In this paper, we introduce a new class of generalized convex function, namely, a-pseudounivex function, by combining the concepts of pseudo-univex and α-invex functions. Further, we establish some relationships between vector variational-like inequality problems and vector optimization problems under the assumptions of α-pseudo-univex functions. Results obtained in this paper present a refinement and improvement of previously known results.     

Exponential distribution-based genetic algorithm for solving mixed-integer bilevel programming problems

Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.     

APPROXIMATE SUBDIFFERENTIALS AND NONSMOOTH ANALYSIS FINITE DIMENSIONS

Ioffe's approximate subdifferentials are reviewed and some of his resultsare generalized.An extension of the calculus of the approximate subdifferentials forthe sums to any finite number of functions is provided along with a generalizationof the Dubovitzkii-Milyutin theorem.The presentation also indicates some of thelimitations of nonsmooth analysis and optimization.Restriction to the class offunction which is suitable for most of the purposes in nonsmooth optimization issuggested.     

Factor analysis of interceptor capture probability

The capture probability of interceptors has been deeply studied.Firstly,the definition of capture probability is analyzed.It is transformed into calculating the probability that the relative position vector between the target and the interceptor locates in a certain cone.The relative position vector and associated covariance matrix are projected in line-of-sight coordinates,and the 3-dimensional integral of a probability function in a cone is calculated to obtain the capture probability.The integral equation is a complicated expression of probability,and it is simplified to an explicit approximate expression according to some assumptions based on the characteristics of the engineering problems.The approximation precision is analyzed by comparative simulation difference,which indicates that approximate assumptions are reasonable.Utilizing the explicit expression,the characteristics of capture probability are analyzed respectively with the factors,such as the distance between the interceptor and the target,the precision of relative position vector,the maximum capture distance and the maximum field angle of interceptor seeker.     

Consensus problem of second-order multi-agent systems with time-varying communication delay and switching topology

Leader-following stationary consensus problem is investigated for the second-order multi-agent systems with timevarying communication delay and switching topology.Based on Lyapunov-Krasovskii functional and Lyapunov-Razumikhin functions respectively,consensus criterions in the form of linear matrix inequality (LMI) are obtained for the system with time-varying communication delays under static interconnection topology converging to the leader’s states.Moreover,the delay-dependent consensus criterion in the form of LMI is also obtained for the system with time-invariant communication delay and switching topologies by constructing Lyapunov-Krasovskii functional.Numerical simulations present the correctness of the results.     

Some Results on Generalized Difference Sets

Sequences with ideal correlation functions have important applications in communications such as CDMA, FDMA, etc. It has been shown that difference sets can be used to construct such sequences. The author extends Pott and Bradley＇s method to a much broader case by proposing the concept of generalized difference sets. Some necessary conditions for the existence of generalized difference sets are established by means of some Diophantine equations. The author also provides an algorithm to determine the existence of generalized difference sets in the cyclic group Zv. Some examples are presented to illustrate that our method works.     

The DY Conjugate Gradient Method with Armijo-type Line Searches

Two Armijo-type line searches are proposed in this paper for nonlinear conjugate gradient methods. The two Armijo-type line searches are shown to guarantee the global convergence of the DY method for the unconstrained minimization of nonconvex differentiable functions. Further, if the function is strictly convex, the two Armijo-type line searches and another Armijo-type line search are also shown to guarantee the convergence of the DY method.     

Statistical Analysis of Two-Parameter Generalized BS-Logistic Fatigue Life Distribution

The logarithmic moment estimations of parameters are proposed for two-parameter generalized Birnbaum-Saunders Logistic fatigue life distribution GBS-Logistic(α, β) under the full sample.The precisions of point estimations are investigated and compared with other point estimations by Monte-Carlo simulations. The approximate interval estimations of parameters are given by using Taylor expansion, and the precisions of approximate interval estimations are investigated by Monte-Carlo simulations. Finally, several examples show the feasibility of the methods.     

Guaranteed cost control for discrete-time networked control systems with random Markov delays

The guaranteed cost control for a class of uncertain discrete-time networked control systems with random delays is addressed.The sensor-to-controller (S-C) and contraller-to-actuator (C-A) random network-induced delays are modeled as two Markov chains.The focus is on the design of a two-mode-dependent guaranteed cost controller,which depends on both the current S-C delay and the most recently available C-A delay.The resulting closed-loop systems are special jump linear systems.Sufficient conditions for existence of guaranteed cost controller and an upper bound of cost function are established based on stochastic Lyapunov-Krasovakii functions and linear matrix inequality (LMI) approach.A simulation example illustrates the effectiveness of the proposed method.     

Necessary conditions for efficient solution of vector optimization problems

In this paper,by using Ljusternik’s theorem and the open mapping theorem of convex process,the author gives necessary conditions for the efficient solution to the vector optimization problems without requiring that the ordering cone in the objective space has a nonempty interior.     

Infrared image segmentation method based on 2D histogram shape modification and optimal objective function

In the methods of image thresholding segmentation,such methods based on two-dimensional(2D) histogram and optimal objective functions are important.However,when they are used for infrared image segmentation,they are weak in suppressing background noises and worse in segmenting targets with non-uniform gray level.The concept of 2D histogram shape modification is proposed,which is realized by target information prior restraint after enhancing target information using plateau histogram equalization.The formula of 2D minimum Renyi entropy is deduced for image segmentation,then the shape-modified 2D histogram is combined with four optimal objective functions(i.e.,maximum between-class variance,maximum entropy,maximum correlation and minimum Renyi entropy) respectively for the application of infrared image segmentation.Simultaneously,F-measure is introduced to evaluate the segmentation effects objectively.The experimental results show that F-measure is an effective evaluation index for image segmentation since its value is fully consistent with the subjective evaluation,and after 2D histogram shape modification,the methods of optimal objective functions can overcome their original forms’ deficiency and their segmentation effects are more or less improvements,where the best one is the maximum entropy method based on 2D histogram shape modification.     

MODELLING RANDOM CONVEX SETS

A model is developed for convex-set valued data,which are the Minkowski sum of aconvex parameter set and a convex noise set.This model is generalized to include location and scaleparameters.A further generalization results in a model for convex sets which is analogous to aone-way analysis of variance models.In each case,estimators of the parameters are given which,under certain conditions,are shown to be consistent.Data generated from the model and theestimators are studied.An outlier detection method is examined.     

GENERALIZED p-VALUES AND GENERALIZED CONFIDENCE INTERVALS FOR VARIANCE COMPONENTS IN GENERAL RANDOM EFFECT MODEL WITH BALANCED DATA

Various random models with balanced data that are relevant for analyzing practical test data are described, along with several hypothesis testing and interval estimation problems concerning variance components. In this paper, we mainly consider these problems in general random effect model with balanced data. Exact tests and confidence intervals for a single variance component corresponding to random effect are developed by using generalized p-values and generalized confidence intervals. The resulting procedures are easy to compute and are applicable to small samples. Exact tests and confidence intervals are also established for comparing the random-effects variance components and the sum of random-effects variance components in two independent general random effect models with balanced data. Furthermore, we investigate the statistical properties of the resulting tests. Finally, some simulation results on the type Ⅰ error probability and power of the proposed test are reported. The simulation results indicate that exact test is extremely satisfactory for controlling type Ⅰ error probability.     

ROBUST STABILITY WITH GUARANTEEING COST FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR PERTURBATION

The problems of robust stability and robust stability with a guaranteeing cost for discrete time-delay systems with nonlinear perturbation are discussed. A sufficient criterion for robust stability is established in an LMI framework and a linear convex optimization problem with LMI constraints for computing maximal perturbation bound is proposed. Meanwhile, a sufficient criterion for robust stability with a guaranteeing cost for such systems is obtained, and an optimal procedure for decreasing the value of guaranteeing cost is put forward. Two examples are used to illustrate the efficiency of the results.     

SUPERCONVERGENCE ANALYSIS OF A NONCONFORMING TRIANGULAR ELEMENT ON ANISOTROPIC MESHES

The class of anisotropic meshes we conceived abandons the regular assumption. Some distinct properties of Carey＇s element are used to deal with the superconvergence for a class of two- dimensional second-order elliptic boundary value problems on anisotropic meshes. The optimal results are obtained and numerical examples are given to confirm our theoretical analysis.     

Adaptive monopulse beamforming with partial parallel structure

A new recursive algorithm with the partial parallel structure based on the linearly constrained minimum variance (LCMV) criterion for adaptive monopulse systems is proposed. The weight vector associated with the original whole antenna array is decomposed into several adaptive weight sub-vectors firstly. An adaptive algorithm based on the conventional LCMV principle is then deduced to update the weight sub-vectors for sum and difference beam, respectively. The optimal weight vector can be obtained after convergence. The required computational complexity is evaluated for the proposed technique, which is on the order of O(N) and less than that of the conventional LCMV method. The flow chart scheme with the partial parallel structure of the proposed algorithm is introduced. This scheme is easy to be implemented on a distributed computer/digital signal processor (DSP) system to solve the problems of the heavy computational burden and vast data transmission of the large-scale adaptive monopulse array. Then, the monopulse ratio and convergence rate of the proposed algorithm are evaluated by numerical simulations. Compared with some recent adaptive monopulse estimation methods, a better performance on computational complexity and monopulse ratio can be achieved with the proposed adaptive method.