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Globally-biased DISIMPL algorithm for expensive global optimization

JOURNAL OF GLOBAL OPTIMIZATION 2014年第2-3期59卷 545-567页

作者： Paulavicius, Remigijus Sergeyev, Yaroslav D. Kvasov, Dmitri E. Zilinskas, Julius Vilnius State Univ Inst Math & Informat LT-08663 Vilnius Lithuania Univ Calabria Dipartimento Ingn Informat Modellist Elettron & S Via P BucciCubo 42C I-87036 Arcavacata Di Rende CS Italy NI Lobachevsky State Univ Software Dept Nizhnii Novgorod Russia

direct-type global optimization algorithms often spend an excessive number of function evaluations on problems with many local optima exploring suboptimal local minima, thereby delaying discovery of the global minimum. In this paper, a globally-biased simplicial partition Disimpl algorithm for global optimization of expensive Lipschitz continuous functions with an unknown Lipschitz constant is proposed. A scheme for an adaptive balancing of local and global information during the search is introduced, implemented, experimentally investigated, and compared with the well-known direct and direct l methods. Extensive numerical experiments executed on 800 multidimensional multiextremal test functions show a promising performance of the new acceleration technique with respect to competitors.

关键词： Global optimization Lipschitz condition direct algorithm Two-phase approach Globally-biased DISIMPL algorithm

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An approach to constrained global optimization based on exact penalty functions

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JOURNAL OF GLOBAL OPTIMIZATION 2012年第2期54卷 251-260页

作者： Di Pillo, G. Lucidi, S. Rinaldi, F. Univ Roma La Sapienza Dipartimento Informat & Sistemist I-00185 Rome Italy

In the field of global optimization many efforts have been devoted to solve unconstrained global optimization problems. The aim of this paper is to show that unconstrained global optimization methods can be used also for solving constrained optimization problems, by resorting to an exact penalty approach. In particular, we make use of a non-differentiable exact penalty function . We show that, under weak assumptions, there exists a threshold value of the penalty parameter such that, for any , any global minimizer of P (q) is a global solution of the related constrained problem and conversely. On these bases, we describe an algorithm that, by combining an unconstrained global minimization technique for minimizing P (q) for given values of the penalty parameter and an automatic updating of that occurs only a finite number of times, produces a sequence {x (k) } such that any limit point of the sequence is a global solution of the related constrained problem. In the algorithm any efficient unconstrained global minimization technique can be used. In particular, we adopt an improved version of the direct algorithm. Some numerical experimentation confirms the effectiveness of the approach.

关键词： Nonlinear programming Global optimization Exact penalty functions direct algorithm

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Separation of sound sources propagated in the same direction

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2005年第7期E88A卷 1665-1672页

作者： Ando, A Iwaki, M Ono, K Kurozumi, K NHK Japan Broadcasting Corp Tokyo 1578501 Japan

This paper describes a method for separating a target sound from other noise arriving in a single direction when the target cannot, therefore, be separated by directivity control. Microphones are arranged in a line toward the sources to form null sensitivity points at given distances from the microphones. The null points exclude non-target sound sources on the basis of weighting coefficients for microphone outputs determined by blind source separation. The separation problem is thereby simplified to instantaneous separation by adjustment of the time-delays for microphone outputs. The system uses a direct (i.e. non-iterative) algorithm for blind separation based on second-order statistics, assuming that all sources are non-stationary signals. Simulations show that the 2-microphone system can separate a target sound with separability of more than 40 dB for the 2-source problem, and 25 dB for the 3-source problem when the other sources are adjacent.

关键词： blind separation of signals independent component analysis microphone system direct algorithm decorrelation

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Application of Reduced-set Pareto-Lipschitzian Optimization to truss optimization

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JOURNAL OF GLOBAL OPTIMIZATION 2017年第1-2期67卷 425-450页

作者： Mockus, Jonas Paulavicius, Remigijus Rusakevicius, Dainius Sesok, Dmitrij Zilinskas, Julius Vilnius Univ Inst Math & Informat Akad 4 LT-08663 Vilnius Lithuania Vilnius Gediminas Tech Univ Sauletekio Al 11 LT-10223 Vilnius Lithuania

In this paper, a recently proposed global Lipschitz optimization algorithm Pareto-Lipschitzian Optimization with Reduced-set (PLOR) is further developed, investigated and applied to truss optimization problems. Partition patterns of the PLOR algorithm are similar to those of Dividing RECTangles (direct), which was widely applied to different real-life problems. However here a set of all Lipschitz constants is reduced to just two: the maximal and the minimal ones. In such a way the PLOR approach is independent of any user-defined parameters and balances equally local and global search during the optimization process. An expanded list of other well-known direct-type algorithms is used in investigation and experimental comparison using the standard test problems and truss optimization problems. The experimental investigation shows that the PLOR algorithm gives very competitive results to other direct-type algorithms

关键词： Truss optimization Lipschitz optimization PLOR algorithm direct algorithm

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A Modified DIviding RECTangles algorithm for a Problem in Astrophysics

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2011年第1期151卷 175-190页

作者： di Serafino, D. Liuzzi, G. Piccialli, V. Riccio, F. Toraldo, G. Univ Naples Federico II Dipartimento Ingn Agr & Agron Terr I-80055 Portici NA Italy Univ Naples 2 Dipartimento Matemat I-81100 Caserta Italy CNR Ist Anal Sistemi & Informat A Ruberti I-00185 Rome Italy Univ Roma Tor Vergata Dipartimento Informat Sistemi & Prod I-00133 Rome Italy

We present a modification of the direct (DIviding RECTangles) algorithm, called direct-G, to solve a box-constrained global optimization problem arising in the detection of gravitational waves emitted by coalescing binary systems of compact objects. This is a hard problem, since the objective function is highly nonlinear and expensive to evaluate, has a huge number of local extrema and unavailable derivatives. direct performs a sampling of the feasible domain over a set of points that becomes dense in the limit, thus ensuring the everywhere dense convergence;however, it becomes ineffective on significant instances of the problem under consideration, because it tends to produce a uniform coverage of the feasible domain, by oversampling regions that are far from the optimal solution. direct has been modified by embodying information provided by a suitable discretization of the feasible domain, based on the signal theory, which takes into account the variability of the objective function. Numerical experiments show that direct-G largely outperforms direct and the grid search, the latter being the reference algorithm in the astrophysics community. Furthermore, direct-G is comparable with a genetic algorithm specifically developed for the problem. However, direct-G inherits the convergence properties of direct, whereas the genetic algorithm has no guarantee of convergence.

关键词： Global optimization direct algorithm Detection of gravitational waves

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A Derivative-Free algorithm for Constrained Global Optimization Based on Exact Penalty Functions

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2015年第3期164卷 862-882页

作者： Di Pillo, Gianni Lucidi, Stefano Rinaldi, Francesco Univ Roma La Sapienza Dipartimento Ingn Informat Automat & Gestionale A I-00185 Rome Italy Univ Padua Dipartimento Matemat I-35121 Padua Italy

Constrained global optimization problems can be tackled by using exact penalty approaches. In a preceding paper, we proposed an exact penalty algorithm for constrained problems which combines an unconstrained global minimization technique for minimizing a non-differentiable exact penalty function for given values of the penalty parameter, and an automatic updating of the penalty parameter that occurs only a finite number of times. However, in the updating of the penalty parameter, the method requires the evaluation of the derivatives of the problem functions. In this work, we show that an efficient updating can be implemented also without using the problem derivatives, in this way making the approach suitable for globally solving constrained problems where the derivatives are not available. In the algorithm, any efficient derivative-free unconstrained global minimization technique can be used. In particular, we adopt an improved version of the direct algorithm. In addition, to improve the performances, the approach is enriched by resorting to derivative-free local searches, in a multistart framework. In this context, we prove that, under suitable assumptions, for every global minimum point there exists a neighborhood of attraction for the local search. An extensive numerical experience is reported.

关键词： Nonlinear optimization Global optimization Exact penalty functions Derivative-free minimization direct algorithm

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Designing PMF with negative tap coefficient

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OPTIK 2014年第4期125卷 1526-1528页

作者： Chen, Lingjian Hou, Fenfei Nanjing Normal Univ Sch Phys Sci & Technol Nanjing 210046 Jiangsu Peoples R China

direct global optimization algorithm is innovatively used in design of PMF. Tap coefficient is attained by achieving direct algorithm with C language and Matlab language is employed to simulate the amplitude response of filters. We have designed PMF (photonic microwave filter) with negative tap coefficient and then optimize the design. The minimum shape factor is as low as 1.3180. The results show that the algorithm is highly efficient in designing filter and can produce necessary passband and stopband response characteristics. In the meantime, transition band becomes steeper in the process of further optimization and the shape factor is closer to 1. (C) 2013 Elsevier GmbH. All rights reserved.

关键词： direct algorithm Photonic microwave filter (PMF) Fiber Bragg grating (FBG)

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COMPUTATION OF CONTINUED FRACTIONS WITHOUT INPUT VALUES

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MATHEMATICS OF COMPUTATION 1995年第211期64卷 1307-1317页

作者： SHIU, P LOUGHBOROUGH UNIV TECHNOL DEPT MATH SCI LOUGHBOROUGH LE11 3TU LEICS ENGLAND

An algorithm for the computation of the continued fraction expansions of numbers which are zeros of differentiable functions is given. The method is direct in the sense that it requires function evaluations at appropriate steps, rather than the value of the number as input in order to deliver the expansion. Statistical data on the first 10000 partial quotients for various real numbers are also given.

关键词： direct algorithm PARTIAL QUOTIENTS KHINTCHINES CONSTANT

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Fuzzy geometric programming (I)

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Fuzzy Sets and Systems 1993年第2期53卷 135-135页

作者： Cao, Bing-yuan Department of Mathematics Changsha Normal University of Water Resources and Electric Power Hunan 410077 China

First, the concepts of fuzzy valuation convex (or concave) function and fuzzy convex-geometric-programming problem are based on a fuzzy valuation set in this paper. Secondly, fuzzy posynomial geometric programming and its dual-form properties concerned are discussed by means of a fuzzy geometric inequality and of a fuzzy dual theory. Lastly, direct and dual algorithms of fuzzy posynomial geometric programming are respectively deduced by the aid of a fuzzy fixed-point theorem and the notion of α, β-cut.

关键词： Fuzzy-valuation sets fuzzy convex (or concave) function fuzzy geometric inequality fuzzy posynomial geometric programming and its dual form direct algorithm dual algorithm

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GAUSSIAN PIVOTING METHOD FORSOLVING LINEAR COMPLEMENTARITY PROBLEM

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Applied Mathematics(A Journal of Chinese Universities) 1997年第4期12卷 419-426页

作者： L1DONGHUI ZengJinping Zhangzhongzhi DepertmentofAppliedMathematics HunanUniversityChangsha410082

In this paper, a new direct algorithm for solving linear complementarity problem with Z-matrix is proposed. The algorithm exhibits either a solution or its nonexistence after at most n steps (where n is the dimension ... 详细信息

关键词： Linear complementarity problem direct algorithm Z-matrix least solution computational complexity

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