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A PRIMAL-DUAL SPLITTING algorithm FOR FINDING ZEROS OF SUMS OF MAXIMAL MONOTONE OPERATORS

SIAM JOURNAL ON OPTIMIZATION 2013年第4期23卷 2011-2036页

作者： Bot, Radu Ioan Csetnek, Erno Robert Heinrich, Andre Univ Vienna Fac Math A-1090 Vienna Austria Tech Univ Chemnitz Dept Math D-09107 Chemnitz Germany

We consider the primal problem of finding the zeros of the sum of a maximal monotone operator and the composition of another maximal monotone operator with a linear continuous operator. By formulating its Attouch-Thera-type dual inclusion problem, a primal-dual splitting algorithm which simultaneously solves the two problems in finite-dimensional spaces is presented. The proposed scheme uses at each iteration the resolvents of the maximal monotone operators involved in separate steps and aims to overcome the shortcoming of classical splitting algorithms when dealing with compositions of maximal monotone and linear continuous operators. The iterative algorithm is used for solving nondifferentiable convex optimization problems arising in image processing and in location theory.

关键词： maximal monotone operator resolvent operator splitting subdifferential minimization algorithm duality

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Characterizations of complete residuated lattice-valued finite tree automata

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FUZZY SETS AND SYSTEMS 2012年 199卷 28-46页

作者： Ghorani, M. Zahedi, M. M. Alzahra Univ Dept Math Tehran Iran Shahid Bahonar Univ Kerman Fac Math & Comp Kerman Iran

This paper deals with the concept of complete residuated lattice-valued (referred to as L-valued) finite tree automata. In this regard, we first define an L-valued regular tree language, and then we prove a necessary and sufficient condition for the regularity of an L-valued tree language. Furthermore, we generalize the pumping lemma for L-valued finite tree automata (L-FTA). Afterwards, the behavior of L-FTA is addressed and some theorems are provided. Moreover, the existence of the minimal form of an L-FTA is considered. Finally, a minimization algorithm of the L-FTA is presented and its time complexity is analyzed. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Non-classical logic Languages Tree automata Pumping lemma L-valued regular tree languages Homomorphism minimization algorithm

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Convergence of solutions to a second order difference inclusion

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2012年第8期75卷 3503-3509页

作者： Khatibzadeh, Hadi Univ Zanjan Dept Math Zanjan Iran

We investigate the asymptotic behavior of solutions to the following second order difference inclusion {u(i+1) - (1 +theta(i))u(i) + theta(i)u(i-1) is an element of c(i)Au(i), i >= 1 u(0) = x, sup(i >= 0)vertical bar u(i)vertical bar < + infinity, where A is a maximal monotone operator in a real Hilbert space H and {c(i)} and {theta(i)} are positive real sequences. We show weak and strong convergence of solutions to an element of A(-1)(0), for general maximal monotone operator and when A = partial derivative phi, where phi is a convex, proper and lower semicontinuous function. Our results extend and improve previous results by Morosanu (1979) [18], Mitidieri-Morosanu (1985-86) [23] (see also Morosanu (1988), [1, pp. 156-168]) and Aperutesei (2003) [21,22], as well as some recent works of Djafari Rouhani-Khatibzadeh (2010, 2011) [25,26] and Khatibzadeh (2011) [27] with more general assumptions on parameters {c(i)} and {theta(i)} in homogeneous case. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Second order difference equation Maximal monotone operator Asymptotic behavior Rate of convergence minimization algorithm

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An Effective Nonsmooth Optimization algorithm for Locally Lipschitz Functions

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2012年第1期155卷 180-195页

作者： Mahdavi-Amiri, Nezam Yousefpour, Rohollah Sharif Univ Technol Fac Math Sci Tehran Iran Univ Mazandaran Dept Math Sci Babol Sar Iran

To construct an effective minimization algorithm for locally Lipschitz functions, we show how to compute a descent direction satisfying Armijo's condition. We present a finitely terminating algorithm to construct an approximating set for the Goldstein subdifferential leading to the desired descent direction. Using this direction, we propose a minimization algorithm for locally Lipschitz functions and prove its convergence. Finally, we implement our algorithm with matrix laboratory (MATLAB) codes and report our testing results. The comparative numerical results attest to the efficiency of the proposed algorithm.

关键词： Armijo's condition Goldstein subdifferential Lipschitz function Search direction minimization algorithm

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Average complexity of Moore's and Hoperoft's algorithms

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THEORETICAL COMPUTER SCIENCE 2012年 417卷 50-65页

作者： David, Julien Univ Paris 13 CNRS LIPN UMR 7030 F-93430 Villetaneuse France

In this paper we prove that for the uniform distribution on complete deterministic automata, the average time complexity of Moore's state minimization algorithm is theta(n log log n), where n is the number of states in the input automata and the number of letters in the alphabet is fixed. Then, an unusual family of implementations of Hoperoft's algorithm is characterized, for which the algorithm will be proved to be always faster than Moore's algorithm. Finally, we present experimental results on the usual implementations of Hoperoft's algorithm. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Finite automata minimization algorithm Moore Hoperoft Average complexity Generic complexity

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Option Price Estimations and Speculative Trading in Knowledge Society

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Procedia Economics and Finance 2012年 3卷 432-437页

作者： Ovidiu Turcoane Bucharest University of Economic Studies 6 Romana Square district 1 Bucharest 010374 Romania

Derivatives market has known an enormous and continuous development from the late 1970s, thanks to the most celebrated Black-Scholes-Merton formula. The impact on global economy is also tremendous, but due to the high leverage of speculative option trading there is a perpetual danger of economical collapse. This paper gives a short description of knowledge society and proposes methods for option price estimation based on implied volatility, skewness and kurtosis. ‘Free-lunch’ is hardly achievable if one predicts the option price using the knowledgeable information from the market and there is almost impossible to speculate, rather than to hedge, when trading option.

关键词： business ethics knowledge society option pricing implied volatility skewness kurtosis minimization algorithm Matlab

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A MONOTONE plus SKEW SPLITTING MODEL FOR COMPOSITE MONOTONE INCLUSIONS IN DUALITY

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SIAM JOURNAL ON OPTIMIZATION 2011年第4期21卷 1230-1250页

作者： Briceno-Arias, Luis M. Combettes, Patrick L. Univ Paris 06 Lab Jacques Louis Lions UMR 7598 F-75005 Paris France

The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally monotone operator and a linear skew-adjoint operator. An algorithmic framework is developed for solving this generic problem in a Hilbert space setting. New primal-dual splitting algorithms are derived from this framework for inclusions involving composite monotone operators, and convergence results are established. These algorithms draw their simplicity and efficacy from the fact that they operate in a fully decomposed fashion in the sense that the monotone operators and the linear transformations involved are activated separately at each iteration. Comparisons with existing methods are made and applications to composite variational problems are demonstrated.

关键词： composite operator convex optimization decomposition duality Fenchel-Rockafellar duality forward-backward-forward algorithm minimization algorithm monotone inclusion monotone operator operator splitting

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Stereo matching: performance study of two global algorithms

Stereo matching: performance study of two global algorithms

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Conference on Radar Sensor Technology XV

作者： Arunagiri, Sarala Jordan, Victor J. Teller, Patricia J. Deroba, Joseph C. Shires, Dale R. Park, Song J. Nguyen, Lam H. Univ Texas El Paso El Paso TX 79968 USA US Army CERDEC Intelligence & Informat Warfare Directore Washington DC 20310 USA US Army Res Lab Adelphi MD USA

ISBN: (纸本)9780819485953

Techniques such as clinometry, stereoscopy, interferometry, and polarimetry are used for Digital Elevation Model (DEM) generation from Synthetic Aperture Radar (SAR) images. The choice of technique depends on the SAR configuration, the means used for image acquisition, and the relief type. The most popular techniques are interferometry for regions of high coherence and stereoscopy for regions such as steep forested mountain slopes. Stereo matching, which is finds the disparity map or correspondence points between two images acquired from different sensor positions, is a core process in stereoscopy. Additionally, automatic stereo processing, which involves stereo matching, is an important process in other applications including vision-based obstacle avoidance for unmanned air vehicles (UAVs), extraction of weak targets in clutter, and automatic target detection. Due to its high computational complexity, stereo matching has traditionally been, and continues to be, one of the most heavily investigated topics in computer vision. A stereo matching algorithm performs a subset of the following four steps: cost computation, cost (support) aggregation, disparity computation/optimization, and disparity refinement. Based on the method used for cost computation, the algorithms are classified into feature-, phase-, and area-based algorithms;and they are classified as local or global based on how they perform disparity computation/optimization. We present a comparative performance study of two pairs, i.e., four versions, of global stereo matching codes. Each pair uses a different minimization technique: a simulated annealing or graph cut algorithm. And, the codes of a pair differ in terms of the employed global cost function: absolute difference (AD) or a variation of normalized cross correlation (NCC). The performance comparison is in terms of execution time, the global minimum cost achieved, power and energy consumption, and the quality of generated output. The results of this

关键词： Stereo matching simulated annealing graph cut minimization algorithm power energy performance

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Controllability criterion for stationary systems

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DOKLADY MATHEMATICS 2010年第1期81卷 6-7页

作者： Zubov, A. V. Dikusar, V. V. Zubov, N. V. Russian Acad Sci Dorodnicyn Comp Ctr Moscow 119333 Russia

The article offers information on the stationary system's controllability criterion. It is discovered that for linear stationary control systems, the minimum amount of control functions where an open system can be created completely controllable. The minimization algorithm is based completely on a partition of the Jordan canonical basis of A into R disjoint groups such that each comprises root vectors of A of a sure height taken once for every eigenvalue λi (i = 1, 2, ..., k) of A. The algorithm suggested lessens a control syste at the stage of its design and selects optimal parameters of the control system.

关键词： DOKLADY Mathematic Robust Stability Observation System Complete Controllability minimization algorithm

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Development of a minimization instrument for allocation of a hospital-level performance improvement intervention to reduce waiting times in Ontario emergency departments

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IMPLEMENTATION SCIENCE 2009年第1期4卷 32-32页

作者： Leaver, Chad Andrew Guttmann, Astrid Zwarenstein, Merrick Rowe, Brian H. Anderson, Geoff Stukel, Therese Golden, Brian Bell, Robert Morra, Dante Abrams, Howard Schull, Michael J. Inst Clin Evaluat Sci Toronto ON Canada Univ Toronto Dept Paediat Toronto ON M5S 1A1 Canada Univ Toronto Dept Hlth Policy Management & Evaluat Toronto ON Canada Sunnybrook Hlth Sci Ctr Ctr Hlth Serv Sci Toronto ON M4N 3M5 Canada Univ Alberta Dept Emergency Med Edmonton AB Canada Univ Alberta Sch Publ Hlth Edmonton AB Canada Univ Toronto Rotman Sch Management Toronto ON Canada Univ Hlth Network Toronto ON Canada Univ Toronto Dept Med Toronto ON Canada Mt Sinai Hosp Toronto ON M5G 1X5 Canada Sunnybrook Hlth Sci Ctr Clin Epidemiol Unit Toronto ON M4N 3M5 Canada

Background: Rigorous evaluation of an intervention requires that its allocation be unbiased with respect to confounders;this is especially difficult in complex, system-wide healthcare interventions. We developed a short survey instrument to identify factors for a minimization algorithm for the allocation of a hospital-level intervention to reduce emergency department (ED) waiting times in Ontario, Canada. Methods: Potential confounders influencing the intervention's success were identified by literature review, and grouped by healthcare setting specific change stages. An international multi-disciplinary (clinical, administrative, decision maker, management) panel evaluated these factors in a two-stage modified-delphi and nominal group process based on four domains: change readiness, evidence base, face validity, and clarity of definition. Results: An original set of 33 factors were identified from the literature. The panel reduced the list to 12 in the first round survey. In the second survey, experts scored each factor according to the four domains;summary scores and consensus discussion resulted in the final selection and measurement of four hospital-level factors to be used in the minimization algorithm: improved patient flow as a hospital's leadership priority;physicians' receptiveness to organizational change;efficiency of bed management;and physician incentives supporting the change goal. Conclusion: We developed a simple tool designed to gather data from senior hospital administrators on factors likely to affect the success of a hospital patient flow improvement intervention. A minimization algorithm will ensure balanced allocation of the intervention with respect to these factors in study hospitals.

关键词： Organizational Change minimization algorithm Nominal Group Technique Candidate Factor minimization Factor

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