• Title/Summary/Keyword: Two-Point Convex Approximation

Search Result 3, Processing Time 0.023 seconds

Design Optimization Using the Two-Point Convex Approximation (이점 볼록 근사화 기법을 적용한 최적설계)

  • Kim, Jong-Rip;Choi, Dong-Hoon
    • Transactions of the Korean Society of Mechanical Engineers A
    • /
    • v.27 no.6
    • /
    • pp.1041-1049
    • /
    • 2003
  • In this paper, a new local two-point approximation method which is based on the exponential intervening variable is proposed. This new algorithm, called the Two-Point Convex Approximation(TPCA), use the function and design sensitivity information from the current and previous design points of the sequential approximate optimization to generate a sequence of convex, separable subproblems. This paper describes the derivation of the parameters associated with the approximation and the numerical solution procedure. In order to show the numerical performance of the proposed method, a sequential approximate optimizer is developed and applied to solve several typical design problems. These optimization results are compared with those of other optimizers. Numerical results obtained from the test examples demonstrate the effectiveness of the proposed method.

Sequential Approximate Optimization by Dual Method Based on Two-Point Diagonal Quadratic Approximation (이점 대각 이차 근사화 기법을 쌍대기법에 적용한 순차적 근사 최적설계)

  • Park, Seon-Ho;Jung, Sang-Jin;Jeong, Seung-Hyun;Choi, Dong-Hoon
    • Transactions of the Korean Society of Mechanical Engineers A
    • /
    • v.35 no.3
    • /
    • pp.259-266
    • /
    • 2011
  • We present a new dual sequential approximate optimization (SAO) algorithm called SD-TDQAO (sequential dual two-point diagonal quadratic approximate optimization). This algorithm solves engineering optimization problems with a nonlinear objective and nonlinear inequality constraints. The two-point diagonal quadratic approximation (TDQA) was originally non-convex and inseparable quadratic approximation in the primal design variable space. To use the dual method, SD-TDQAO uses diagonal quadratic explicit separable approximation; this can easily ensure convexity and separability. An important feature is that the second-derivative terms of the quadratic approximation are approximated by TDQA, which uses only information on the function and the derivative values at two consecutive iteration points. The algorithm will be illustrated using mathematical and topological test problems, and its performance will be compared with that of the MMA algorithm.

APPROXIMATION OF CONVEX POLYGONS

  • Lee, Young-Soo
    • Journal of applied mathematics & informatics
    • /
    • v.10 no.1_2
    • /
    • pp.245-250
    • /
    • 2002
  • Consider the Convex Polygon Pm={Al , A2, ‥‥, Am} With Vertex points A$\_$i/ = (a$\_$i/, b$\_$i/),i : 1,‥‥, m, interior P$\^$0/$\_$m/, and length of perimeter denoted by L(P$\_$m/). Let R$\_$n/ = {B$_1$,B$_2$,‥‥,B$\_$n/), where B$\_$i/=(x$\_$i/,y$\_$I/), i =1,‥‥, n, denote a regular polygon with n sides of equal length and equal interior angle. Kaiser[4] used the regular polygon R$\_$n/ to approximate P$\_$m/, and the problem examined in his work is to position R$\_$n/ with respect to P$\_$m/ to minimize the area of the symmetric difference between the two figures. In this paper we give the quality of a approximating regular polygon R$\_$n/ to approximate P$\_$m/.