JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vot. I7, Nos. 3]4, t975 TECHNICAL NOTE A Note on the Optimization of Constrained Design Problems 1 G . STEPHANOPOULOS 2 Communicated by D. G. Luenberger Abstract. This paper describes a new algorithm for solving con- strained optimization problems, based on a method proposed by Chattopadhyay. The proposed algorithm replaces the original problem with m constraints, m > 1, by a sequence of optimization problems, with one constraint. Here, we modify the algorithm given by Chattopadhyay in order to make it applicable for a larger class of optimization problems and to improve its convergence characteristics. Key Words. Bounds on cost functionats, engineering design, in- equality constraints, mathematical programming, penalty-function methods. 1. Introduction The constrained optimization problem has attracted the attention of many researchers during the last decade, and major developments towards the solution of the problem have been made. A very interesting approach to handle a large number of constraints has been proposed by Chattopadhyay (Ref. 1). The proposed method replaces the original optimization problem with m constraints, m ~ 1, by a sequence of optimization problems with one constraint. The theory behind this method is as follows. 1 Partial support from the Graduate School of the University of Minnesota is gratefully acknowledged. 2 Assistant Professor, Department of Chemical Engineering and Materials Science~ Universit3~ of Minnesota, Minneapolis, Minnesota. 337 © 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of this publication may be reprodliced, stored in a retrieval system~ or transmitted, in any form or by any means, electronic mechanical, ph6toeopying, microfilming, recording, or otherwise, without wr/tten permission of the publisher.