Computer Program Descriptions

DESCRIPTION : To solve design problems in which the objective is to best satisfy a given set of design specifications or constraints in the least @h or minimax sense, assuming the availability of first partial derivatives of the functions concerned with respect to the design parameters. Fortran IV; 512 cards, including comments. J. W. Bandler is with the Department of Electrical Engineering, McMaster University, Hamilton, Ont., Canada. C. Charalambous is with the Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ont., Canada, J, H, K. Chen is with Bell-Northern Research, Ottawa, Ont,, Canada. ASIS/NAPS Document No, NAPS 02812. Listing and user’s manual also available from J. W. Bandler at $15.00. Source deck available for $50,00, This program, called MINOPT, was used to generate some of the results presented in a recent paper [1]. The aim is to meet or exceed design specifications using the least @h approach [1][7 ], in particular, by an implementation of further results by Charalambous [7]. We assume the availability of first partial derivatives of the functions concerned with respect to the design parameters, Essentially, a single least pth approximation with 1 < p < m can be done, or a sequence of least ,pth approximations with tiite constant p can b? carried out to produce highly accurate minimax solutions, if desired. The algorithm employs a lower bound on the minimax solution based on convexity assumptions and estimated after each least pth solution is reached. ,This lower bound can also be optionally used to provide a basis for successively dropping functions likely to be inactive at the solution, to reduce computational effort. Furthermore, gradient evaluations are usually not required for all the functions retained at any one time. Fletcher’s quasi-Newton program [8] is used to minimize the unconstrained objective resulting from our formulation. Restarting or rerunning the program making use of the results of a previous run with the same problem is a simple and useful feature. If the problem involves meeting certain design specifications, the first optimization will indicate whether such specifications can be satisfied [4][6 ]. An option is provided to