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ArITHMETIC MODELING OF rANDOM PrOCESSES AND r-algorithmS

CYBErNETICS AND SYSTEMS ANALYSIS 2012年第1期48卷 17-25页

作者： Glazunov, N. M. Natl Aviat Univ Kiev Ukraine

Three classes of methods to generate pseudorandom sequences based on arithmetic principles are given. A class of matrix nondifferentiable optimization problems is analyzed and a method is proposed to solve them based ... 详细信息

关键词： nondifferentiable optimization stochastic approximation of a random process uniform distribution with prescribed density r-algorithm matrix optimization

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THEOrY AND SOFTWArE IMPLEMENTATIONS OF SHOr'S r-algorithmS

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CYBErNETICS AND SYSTEMS ANALYSIS 2017年第5期53卷 692-703页

作者： Stetsyuk, P. I. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine

Three computational forms of r-algorithms with different amount of computation per iteration are considered. The results on the convergence of the limit variant of r-algorithms for convex smooth functions and the r (mu) (alpha)-algorithm for convex piecewise smooth functions are presented. Practical aspects of the variant of r (alpha)-algorithms with a constant coefficient of space dilation alpha and an adaptive method for step adjustment in the direction of the normalized anti-subgradient in the transformed space of variables are discussed.

关键词： subgradient method steepest descent difference of subgradients space dilation r-algorithm conjugate gradient method adaptive step software implementation

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Constructing the External Contour of the Frankl Nozzle Using S-Shaped Curves with Quadratic Distribution of the Curvature

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CYBErNETICS AND SYSTEMS ANALYSIS 2020年第6期56卷 963-977页

作者： Stetsyuk, P. I. Tkachenko, O. V. Khomyak, O. M. Gritsay, O. L. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine Ivchenko Progress ZMKB Zaporizhzhia Ukraine

A mathematical model, an algorithm, and a software are developed for the problem of constructing an S-shaped curve passing through two given points with specified tangent inclination angles and providing a tangent inclination angle at a point with a given abscissa. To control the inflection point of the S-shaped curve with quadratic distribution of curvature in natural parameterization, the tangent inclination angle at the point with the known abscissa is used. The algorithm is based on the modification of the method with space dilation in the direction of the difference of two successive generalized gradients. Computational experiments have shown the efficiency of the developed algorithm for constructing the external contour of a Frankl-type nozzle.

关键词： external nozzle contour S-shaped curve natural parameterization quadratic curvature nonsmooth optimization r-algorithm

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Sparse Balanced Layout of Spherical Voids in Three-Dimensional Domains

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CYBErNETICS AND SYSTEMS ANALYSIS 2021年第4期57卷 542-551页

作者： Stoyan, Y. G. romanova, T. E. Pankratov, O., V Stetsyuk, P., I Stoian, Y. E. Natl Acad Sci Ukraine A Pidhornyi Inst Mech Engn Problems Kiev Ukraine Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine

The authors consider the optimization problem of layout of spherical voids in three-dimensional domains bounded by cylindrical and spherical surfaces and planes. The problem is reduced to arranging spherical objects in a composite container, with regard for the constraints on their "sparseness" and balance conditions (location of the gravity center of the system). A mathematical model in the form of a nonlinear programming problem is constructed. A method of fast search for feasible solutions based on the balanced homothetic transformations of 3D objects and methods of finding locally optimal solutions using the decomposition algorithm and r-algorithm are proposed. The results of numerical experiments are provided.

关键词： sparse layout spherical objects phi-function nonlinear programming r-algorithm

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Nonsmooth-optimization methods in problems of stochastic programming

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CYBErNETICS AND SYSTEMS ANALYSIS 1999年第5期35卷 708-720页

作者： Shor, NZ Bardadym, TA Zhurbenko, NG Lykhovid, AP Stetsyuk, PI Natl Acad Sci Ukraine Inst Cybernet Kiev Ukraine

Nonsmooth-optimization methods with space expansion are considered as applied to decomposition schemes realized in solving two-stage problems of stochastic programming in the SLP-IOr simulation system.

关键词： nonsmooth optimization decomposition recourse stochastic programming SLP-IOr simulation systems r-algorithm

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ON N. Z. SHOr'S THrEE SCIENTIFIC IDEAS

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CYBErNETICS AND SYSTEMS ANALYSIS 2012年第1期48卷 2-16页

作者： Sergienko, I. V. Stetsyuk, P. I. Natl Acad Sci Ukraine VM Glushkov Cybernet Inst Kiev Ukraine

The paper is devoted to the 75th anniversary of the Kyiv mathematician Naum Shor and is focused on his three central ideas: generalized gradient descent (1962), the use of linear nonorthogonal space transformations to improve the conditionality of ravine functions (1969), and dual approach for finding bounds of the objective function in nonconvex quadratic models (1985). Examples of the application of these ideas in methods and algorithms developed at the V. M. Glushkov Institute of Cybernetics of the NAS of Ukraine are given.

关键词： nondifferentiable optimization subgradient method space dilation operator ellipsoid method r-algorithm quadratic extremum problem dual estimate functionally redundant constraints

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Stereoscopic Image Coding Using a Global Disparity Estimation algorithm Optimizing the Compensation Scheme Impact 24

Stereoscopic Image Coding Using a Global Disparity Estimatio...

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24th IEEE Conference on Signal Processing: algorithms, Architectures, Arrangements, and Applications (IEEE SPA)

作者： Kadri, Imen Dauphin, Gabriel Mokraoui, Anissa Lachiri, Zied Univ Sorbonne Paris Nord L2TI UR 3043 F-93430 Villetaneuse France Univ Tunis El Manar LSITI Ecole Natl Ingenieur Tunis Tunis Tunisia

ISBN: (纸本)9788362065394

This paper focuses on the disparity-compensated stereoscopic image coding. This coding scheme is the most implemented technique taking advantage of the typical stereoscopic image redundancy. Namely it first predicts one view using the other view and a disparity map. A compensated view is then computed by coding the remaining difference between the view and its prediction. This paper concerns the computation of the disparity map combining two existing techniques. The first one, more efficient at low bitrate, is an iterative search reducing the bit cost of losslessly storing the disparity map at the expense of a small increase in distortion. The second one, more efficient at high bitrate, selects disparities minimizing the distortions of the compensated view, assuming that JPEG is used in the compensation. This combination appears to be fruitful, achieving increased performance at low- and mid-range bitrate, when tested on a few stereoscopic images and compared to these two techniques.

关键词： Stereoscopic Image Coding Block-Matching algorithm Disparity Disparity-Compensation r-algorithm FDCBM-algorithm JPEG

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Equivalence Knowledge Cumularspharolith and IV-type Completeness of the Knowledge Base K in r-logic C_r

Equivalence Knowledge Cumularspharolith and IV-type Complete...

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1st WrI Global Congress on Intelligent Systems (GCIS 2009)

作者： Zheng, Yalin Li, Yong Dongguan Univ Sci & Technol Dept Comp Sci & Technol Fac Software Res Ctr Intelligent Informat Technol Dongguan 523808 Peoples R China

ISBN: (纸本)9780769535715

By casting off the direct restriction of topological structure, this paper presents another matching scheme between the input A* and the knowledge A -> B based on the equivalence relation r. on formulae set F(S) and the corresponding equivalence classification F(S)/r = {[A](r)|A is an element of F(S)} therefore, obtains another algorithm of approximate reasoning the IV-type r-algorithm. The paper presents the IV-type completeness and the IV-type perfection of the knowledge base K in r logic C-r and regular r-logic C-r.

关键词： Approximate reasoning Pseudo-distance Formulae Cumularspharolith Knowledge Cumularspharolith Approximate Knowledge Closure of Knowledge Base r-logic r-algorithm r-completeness

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Limited Memory Space Dilation and reduction algorithms

Limited Memory Space Dilation and Reduction Algorithms

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作者： Ansari, Zafar A. Virginia Tech | University

In this thesis, we present variants of Shor and Zhurbenko’s r-algorithm, motivated by the memoryless and limited memory updates for differentiable quasi-Newton methods. This well known r-algorithm, which employs a space dilation strategy in the direction of the difference between two successive subgradients, is recognized as being one of the most effective procedures for solving nondifferentiable optimization problems. However, the method needs to store the space dilation matrix and update it at every iteration, resulting in a substantial computational burden for large-sized problems. To circumvent this difficulty, we first develop a memoryless update scheme. In the space transformation sense, the new update scheme can be viewed as a combination of space dilation and reduction operations. We prove convergence of this new algorithm, and demonstrate how it can be used in conjunction with a variable target value method that allows a practical, convergent implementation of the method. For performance comparisons we examine other memoryless and limited memory variants, and also prove a modification of a related algorithm due to Polyak that employs a projection on a pair of Kelley’s cutting planes. These variants are tested along with Shor’s r-algorithm on a set of standard test problems from the literature as well as on randomly generated dual transportation and assignment problems. Our computational experiments reveal that the proposed memoryless space dilation and reduction algorithm (VT-MSDr) and the proposed modification of the Polyak-Kelly cutting plane method (VT-PKC) provide an overall competitive performance relative to the other methods tested with respect to solution quality and computational effort. The r-algorithm becomes increasingly more expensive with an increase in problem size, while not providing any gain in solution quality. The fixed dilation (with no reduction) strategy (VT-MSD) provides a comparable, though second-choice, alternative to VT-MSDr. Emp

关键词： Nondifferentiable Optimization Space Dilation r-algorithm Subgradient Optimization Thesis

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