editorial stochastic optimization: theory and applications

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2013, Article ID 949131, 2 pageshttp://dx.doi.org/10.1155/2013/949131

EditorialStochastic Optimization: Theory and Applications

Bin Wang,1 Lotfollah Najjar,2 Neal N. Xiong,3 and Rung Ching Chen4

1 Engineering Optimization and Smart Antenna Institute, School of Computer and Communication Engineering,Northeastern University at Qinhuangdao, Hebei, Qinhuangdao 066004, China

2 Information System Quantitative Analysis, College of Information Science & Technology (IS&T),University of Nebraska at Omaha, Omaha, NE 68182, USA

3 School of Computer Science, Colorado Technical University, 4435 North Chestnut Street, Colorado Springs, CO 80907, USA4College of Informatics Chaoyang University of Technology, 168 Jifong East Road, Wufong District, Taichung City 41349, Taiwan

Correspondence should be addressed to Bin Wang; [email protected]

Received 23 October 2013; Accepted 23 October 2013

Copyright © 2013 Bin Wang et al.This is an open access article distributed under theCreativeCommonsAttribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

As an important branch of applied mathematics, optimiza-tion theory, especially stochastic optimization, becomes animportant tool for solving multiobjective decision-makingproblems in random process recently. Many kinds of indus-trial, biological, engineering, and economic problems can beviewed as stochastic systems, for example, area of communi-cation, gene, signal processing, geography, civil engineering,aerospace, banking, and so forth. Stochastic optimizationis suitable to solve the decision-making problems in thesestochastic systems.

This special issue includes 16 high-quality peer-reviewedpapers that deal with different aspects of stochastic optimiza-tion problems. These papers contain some new, novel, andinnovative techniques and ideas. We hope that all the paperspublished in this special issue can stimulate the continuingefforts to understand this field, particularly new stochasticoptimization algorithms and new applications in relatedfields.

In the paper entitled “Qualitative and quantitative inte-grated modeling for stochastic simulation and optimization,”the authors propose a qualitative and quantitative combinedmodeling specification based on a hierarchical model struc-ture framework. The new modeling approach is based on ahierarchical model structure which includes the meta-metamodel, the metamodel, and the high-level model.

In the paper entitled “Estimating time-varying beta of pricelimits and its applications in China stock market,” the authorspropose an estimation method of time-varying beta of price

limits. It uses China stock market trading data to estimatetime-varying beta and researches on systemic risk in Chinastock market.

In the paper entitled “Doubly constrained robust blindbeamforming algorithm,” the authors propose doubly con-strained robust least squares constant modulus algorithm(LSCMA) to solve the problem of signal steering vectormismatches via the Bayesian method and worst-case per-formance optimization, which is based on the mismatchesbetween the actual andpresumed steering vectors. A theoreti-cal analysis for the proposed algorithm in terms of complexitycost, convergence performance, and SINR performance ispresented in this paper.

In the paper entitled “Smoothing techniques and aug-mented Lagrangian method for recourse problem of two-stage stochastic linear programming,” the authors apply thesmoothing techniques and a fast Newton-Armijo algorithmfor solving an unconstrained smooth reformulation of thisproblem. Computational results and comparisons are givento show the effectiveness and speed of the algorithm.

In the paper entitled “New results on robust stability andstabilization of linear discrete-time stochastic systems with con-vex polytopic uncertainties,” the authors propose new delay-dependent mean square robust stability conditions for linearpolytopic delay-difference stochastic equations with intervaltime-varying delays in terms of LMIs. An application torobust stabilization of linear discrete-time stochastic controlsystems is given in this paper.

2 Journal of Applied Mathematics

In the paper entitled “Layer-based data aggregation andperformance analysis in wireless sensor networks,” the authorsfocus on theminimum-latency data aggregation problem andpropose a new efficient scheme for it.The basic idea is to buildan aggregation tree by ordering nodes into layers and then usea scheduling algorithm on the basis of the aggregation treeto determine the transmission time slots for all nodes in thenetwork with collision avoiding.

In the paper entitled “Optimal waveform selection forrobust target tracking,” the authors assume a one-dimensiontarget model which will try to escape the radar detectionto degrade the tracking performance and propose a newoptimal waveform selection algorithm based on game theoryfor robust tracking. The optimal parameters for transmittedwaveform are finally found by the minimization of the traceof the estimated state error covariance.

In the paper entitled “Adaptive waveform design formultiple radar tasks based on constantmodulus constraint,” theauthors propose a waveform design method which can effi-ciently synthesize waveforms and provide a trade-off betweenestimation performance and detection performance and thenapply the technique of generating a constant modulus signalwith the given Fourier transformmagnitude to thewaveform.Finally a waveform that has constant modulus property canbe obtained.

In the paper entitled “Univex interval-valued mappingwith differentiability and its application in nonlinear program-ming,” the authors introduce interval-valued univex func-tions for differentiable programming problems and deriveoptimality and duality results for a class of generalizedconvex optimization problems with interval-valued univexfunctions.

In the paper entitled “Study on indefinite stochastic linearquadratic optimal control with inequality constraint,” theauthors study the indefinite stochastic LQ optimal controlproblem with unequally terminal state constraint, whichcan be transformed into a hybrid constrained mathematicalprogramming problem and design a dynamic programmingalgorithm to solve the constrained indefinite stochastic LQissue.

In the paper entitled “A fast optimization method forreliability and performance of cloud services compositionapplication,” the authors propose a fast optimization methodfor reliability and performance of cloud services compositionapplication based on Universal Generating Function andGenetic Algorithm.The model and algorithm can be appliedin online prediction and optimization for reliability andperformance of cloud services composition application.

In the paper entitled “Dynamicmean-variancemodel withborrowing constraint under the constant elasticity of varianceprocess,” the authors study a continuous-time dynamicmean-variance portfolio selection problem with the constraint of ahigher borrowing rate, in which stock price is governed by aconstant elasticity of variance (CEV) process.

In the paper entitled “An improved hybrid genetic algo-rithm with a new local search procedure,” the authors proposea novel, simplified, and efficient HGA with a new individuallearning procedure that performs a LS only when the bestoffspring (solution) in the offspring population is also the

best in the current parent population and develop a new LSmethod based on a three-directional search (TD), which isderivative-free and self-adaptive.

In the paper entitled “Reflected backward stochastic differ-ential equations driven by countable brownian motions,” theauthors deal with a new class of reflected backward stochasticdifferential equation driven by countable Brownian motions.The existence and uniqueness of the RBSDEs is obtained viaSnell envelope and fixed theorem.

In the paper entitled “Pareto optimal solutions for stochas-tic dynamic programming problems via Monte Carlo sim-ulation,” the authors propose a heuristic algorithm for aclass of stochastic discrete-time continuous-variable dynamicprogramming problems submitted to non-Gaussian dis-turbances. This new idea is carried out by using MonteCarlo simulations embedded in an approximate algorithmproposed for deterministic dynamic programming problems.The new method is tested in instances of the classicalinventory control problem.

In the paper entitled “On iterative learning control forremote control systems with packet loss,” the authors proposean ILC for a time-varying system with random packetdropouts. The ILC law adopts an iteration-average operatorand a revised learning gain that takes into consideration theprobabilities of data-dropout factors.

Acknowledgments

As guest editors for this special issue, we would like to takethis opportunity to thank all the contributions from theauthors and reviewers. BinWang was supported by the Natu-ral Science Foundation of Hebei Province (no. F2013501075),the Doctoral Scientific Research Foundation of LiaoningProvince (no. 20131030), and the Fundamental ResearchFunds for the Central Universities (no. N110323005).

Bin WangLotfollah NajjarNeal N. Xiong

Rung Ching Chen

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