• 대한수학회지
• /
• 제47권4호
• /
• pp.767-788
• /
• 2010

In this paper, we propose two limited memory BFGS algorithms with a nonmonotone line search technique for unconstrained optimization problems. The global convergence of the given methods will be established under suitable conditions. Numerical results show that the presented algorithms are more competitive than the normal BFGS method.

• Journal of applied mathematics & informatics
• /
• 제23권1_2호
• /
• pp.311-319
• /
• 2007

This article studies a modified BFGS algorithm for solving smooth unconstrained strongly convex minimization problem. The modified BFGS method is based on the new quasi-Newton equation $B_k+1{^s}_k=yk\;where\;y_k^*=yk+A_ks_k\;and\;A_k$ is a matrix. Wei, Li and Qi [WLQ] have proven that the average performance of two of those algorithms is better than that of the classical one. In this paper, we prove the global convergence of these algorithms associated to a general line search rule.

• Journal of applied mathematics & informatics
• /
• 제28권5_6호
• /
• pp.1239-1248
• /
• 2010

In this paper, an implementable BFGS bundle algorithm for solving a nonsmooth convex optimization problem is presented. The typical method minimizes an approximate Moreau-Yosida regularization using a BFGS algorithm with inexact function and the approximate gradient values which are generated by a finite inner bundle algorithm. The approximate subgradient of the objective function is used in the algorithm, which can make the algorithm easier to implement. The convergence property of the algorithm is proved under some additional assumptions.

• 대한토목학회논문집
• /
• 제12권1호
• /
• pp.197-205
• /
• 1992

혼성방파제단면의 최적설계를 위해, ALM-BFGS 조합알고리즘을 이용한 컴퓨터 프로그램 PROCOBRA가 개발되었다. 혼성방파제의 단면최적화를 위한 정식화의 모형이 제시되었으며 단면의 부분별 가중치가 목적함수에 도입되었다 수치예를 통하여 프로그램의 유용성이 입증되었다. 연구결과 ALM-BFGS 알고리즘이 해안구조물의 최적설계에 효율적으로 적용될 수 있으며, 경제적인 혼성방파제 설계가 가능함을 알 수 있었다.

• Journal of applied mathematics & informatics
• /
• 제16권1_2호
• /
• pp.195-205
• /
• 2004

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the quasi-Newton iteration pattern. We prove the global convergence properties of the algorithm associating with the general form of line search, and prove the quadratic convergence rate of the algorithm under some conditions.

• 대한조선학회지
• /
• 제23권3호
• /
• pp.39-44
• /
• 1986

The basic BFGS procedure for the nonlinear finite element analysis is reviewed. Through a simple numerical example, promising characteristics of the method evaluated discussed. Based on the discussion of computational performance, a modified BFGS algorithm with substructuring is derived and proposed for the quasi-static analysis of large-scale nonlinear structures.

• Journal of applied mathematics & informatics
• /
• 제22권1_2호
• /
• pp.193-208
• /
• 2006

A modified BFGS algorithm for solving the unconstrained optimization, whose Hessian matrix at the minimum point of the convex function is of rank defects, is presented in this paper. The main idea of the algorithm is first to add a modified term to the convex function for obtain an equivalent model, then simply the model to get the modified BFGS algorithm. The superlinear convergence property of the algorithm is proved in this paper. To compared with the Tensor algorithms presented by R. B. Schnabel (seing [4],[5]), this method is more efficient for solving singular unconstrained optimization in computing amount and complication.

• 충청수학회지
• /
• 제21권1호
• /
• pp.117-127
• /
• 2008

The performance of a modified Armijo line search rule related to BFGS gradient type method with the results from other well-known line search rules are compared as well as analyzed. Although the modified Armijo rule does require as much computational cost as the other rules, it shows more efficient in finding local minima of unconstrained optimization problems. The sensitivity of the parameters used in the line search rules is also analyzed. The results obtained by implementing algorithms in Matlab for the test problems in [3] are presented.

• Journal of applied mathematics & informatics
• /
• 제24권1_2호
• /
• pp.325-331
• /
• 2007

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm associated with the general line search model. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the new quasi-Newton iteration equation $B_{k+1}s_k=y^*_k,\;where\;y^*_k$ is the sum of $y_k\;and\;A_ks_k,\;and\;A_k$ is some matrix. The global convergence properties of the algorithm associating with the general form of line search is proved.

• 한국음향학회지
• /
• 제19권1호
• /
• pp.25-31
• /
• 2000

이 논문에서는 직적법을 이용하여 반복법인 BFGS법의 초기값을 설정하는 알고리즘을 제안하고, 이를 이용하여 점배열음원 형태의 적응형 초음파 트랜스듀서의 최적 지향성합성을 시도했다. 이의 유효성을 확인하기 위하여 부엽의 레벨을 -30dB 이하로 제한한 임의의 빔폭을 갖는 준이상 빔, 회전 빔, 그리고 다중 빔을 보기로 하여 점배열음원으로 형성되는 2차원 음장내의 지향성합성 문제 및 복수의 주파수에 대한 적응 지향성합성 시스템의 적응성 문제를 검토하였다. 수치계산 결과, 제안한 방법은 BFGS법 단독에 의한 지향성합성보다 수렴속도가 빠르고, 목적 지향성합성을 위한 오차개선도 탁월하며, BFGS법과 같은 반복법에서 문제가 되는 초기치의 선택이 필요하지 않다는 장점도 있다. 또한, 제안법은 직접법 단독으로는 불가능한 적응제어도 가능하다.