• 제목/요약/키워드: Unconstrained optimization

검색결과 126건 처리시간 0.02초

A NEW CLASS OF NONLINEAR CONJUGATE GRADIENT METHOD FOR UNCONSTRAINED OPTIMIZATION MODELS AND ITS APPLICATION IN PORTFOLIO SELECTION

  • Malik, Maulana;Sulaiman, Ibrahim Mohammed;Mamat, Mustafa;Abas, Siti Sabariah;Sukono, Sukono
    • Nonlinear Functional Analysis and Applications
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    • 제26권4호
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    • pp.811-837
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    • 2021
  • In this paper, we propose a new conjugate gradient method for solving unconstrained optimization models. By using exact and strong Wolfe line searches, the proposed method possesses the sufficient descent condition and global convergence properties. Numerical results show that the proposed method is efficient at small, medium, and large dimensions for the given test functions. In addition, the proposed method was applied to solve practical application problems in portfolio selection.

GLOBAL CONVERGENCE OF A NEW SPECTRAL PRP CONJUGATE GRADIENT METHOD

  • Liu, Jinkui
    • Journal of applied mathematics & informatics
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    • 제29권5_6호
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    • pp.1303-1309
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    • 2011
  • Based on the PRP method, a new spectral PRP conjugate gradient method has been proposed to solve general unconstrained optimization problems which produce sufficient descent search direction at every iteration without any line search. Under the Wolfe line search, we prove the global convergence of the new method for general nonconvex functions. The numerical results show that the new method is efficient for the given test problems.

CONVERGENCE OF THE NONMONOTONE PERRY-SHANNO METHOD FOR UNCONSTRAINED OPTIMIZATION

  • Ou, Yigui;Ma, Wei
    • Journal of applied mathematics & informatics
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    • 제30권5_6호
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    • pp.971-980
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    • 2012
  • In this paper, a method associating with one new form of nonmonotone linesearch technique is proposed, which can be regarded as a generalization of the Perry-Shanno memoryless quasi-Newton type method. Under some reasonable conditions, the global convergence of the proposed method is proven. Numerical tests show its efficiency.

A CLASS OF NONMONOTONE SPECTRAL MEMORY GRADIENT METHOD

  • Yu, Zhensheng;Zang, Jinsong;Liu, Jingzhao
    • 대한수학회지
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    • 제47권1호
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    • pp.63-70
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    • 2010
  • In this paper, we develop a nonmonotone spectral memory gradient method for unconstrained optimization, where the spectral stepsize and a class of memory gradient direction are combined efficiently. The global convergence is obtained by using a nonmonotone line search strategy and the numerical tests are also given to show the efficiency of the proposed algorithm.

CONVERGENCE OF SUPERMEMORY GRADIENT METHOD

  • Shi, Zhen-Jun;Shen, Jie
    • Journal of applied mathematics & informatics
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    • 제24권1_2호
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    • pp.367-376
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    • 2007
  • In this paper we consider the global convergence of a new super memory gradient method for unconstrained optimization problems. New trust region radius is proposed to make the new method converge stably and averagely, and it will be suitable to solve large scale minimization problems. Some global convergence results are obtained under some mild conditions. Numerical results show that this new method is effective and stable in practical computation.

진동응답을 최소화하는 비구속형 제진보의 제진 부위 최적설계 (Optimal Treatment of Unconstrained Visco-elastic Damping Layer on Beam to Minimize Vibration Responses)

  • 이두호
    • 한국소음진동공학회논문집
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    • 제15권7호
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    • pp.829-835
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    • 2005
  • An optimization formulation of unconstrained damping treatment on beam is proposed to minimize vibration responses using a numerical search method. The fractional derivative model is combined with RUK's equivalent stiffness approach in order to represent nonlinearity of complex modulus of damping materials with frequency and temperature. Vibration responses are calculated by using the modal superposition principle, and of which design sensitivity formula with respect to damping layout is derived analytically. Plugging the sensitivity formula into optimization software, we can determine optimally damping treatment region that gives minimum forced response under a given boundary condition. A numerical example shows that the proposed method is very effective in suppressing nitration responses by means of unconstrained damping layer treatment.

CONVERGENCE PROPERTIES OF A CORRELATIVE POLAK-RIBIERE CONJUGATE GRADIENT METHOD

  • Hu Guofang;Qu Biao
    • Journal of applied mathematics & informatics
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    • 제22권1_2호
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    • pp.461-466
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    • 2006
  • In this paper, an algorithm with a new Armijo-type line search is proposed that ensure global convergence of a correlative Polak-Ribiere conjugate method for the unconstrained minimization of non-convex differentiable function.

수정된 유전 알고리즘을 이용한 비선형최적화 문제의 효율적인 해법 (An efficient method for nonlinear optimization problems using modified genetic algorithms)

  • 윤영수;이상용
    • 한국경영과학회:학술대회논문집
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    • 대한산업공학회/한국경영과학회 1996년도 춘계공동학술대회논문집; 공군사관학교, 청주; 26-27 Apr. 1996
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    • pp.519-524
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    • 1996
  • This paper describes the application of Genetic Algorithms(GAs) to nonlinear constrained mixed optimization problems. Genetic Algorithms are combinatorial in nature, and therefore are computationally suitable for treating discrete and integer design variables. But, several problems that conventional GAs are ill defined are applicaiton of penalty function that can be adapted to transform a constrained optimization problem into an unconstrained optimization problem into an unconstrained one and premature convergence of solution. Thus, we developed an modified GAs to solve this problems, and two examples are given to demonstrate the effectiveness of the methodology developed in this paper.

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A NOTE ON OPTIMIZATION WITH MORSE POLYNOMIALS

  • Le, Cong-Trinh
    • 대한수학회논문집
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    • 제33권2호
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    • pp.671-676
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    • 2018
  • In this paper we prove that the gradient ideal of a Morse polynomial is radical. This gives a generic class of polynomials whose gradient ideals are radical. As a consequence we reclaim a previous result that the unconstrained polynomial optimization problem for Morse polynomials has a finite convergence.

제한조건이 없는 최적화 문제의 강건설계에 관한 연구 (A Study on the Robust Design for Unconstrained Optimization Problems)

  • 이권희;엄인섭;이완익
    • 대한기계학회논문집
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    • 제18권11호
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    • pp.2825-2836
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    • 1994
  • The engineering optimization has been developed for the automatic design of engineering systems. Since the conventional optimum is determined without considering noise factors, applications to practical problems can be limited. Current design practice tends to account for these noises by the specification of closer tolerances or the use of safety factors. However, these approaches may be very expensive. Thus the consideration on the noises of design variables is needed for optimal design. A method is presented to find robust solutions for unconstrained optimization problems. The method is applied to discrete and continuous variables. The orthogonal array is utilized based on the Taguchi concept. Through mathematical proofs and numerical examples, it is verified that solutions from the suggested method are more insensitive than the conventional optimum within the range of variations for design variables.