A Sequential Linearization Approach for Solving Mixed-Discrete Nonlinear Design Optimization Problems

[+] Author and Article Information
Han Tong Loh

Department of Mechanical and Production Engineering, National University of Singapore, Singapore

P. Y. Papalambros

Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, MI 48109

J. Mech. Des 113(3), 325-334 (Sep 01, 1991) (10 pages) doi:10.1115/1.2912786 History: Received May 01, 1990; Online June 02, 2008


Design optimization models of often contain variables that must take only discrete values, such as standard sizes. Nonlinear optimization problems with a mixture of discrete and continuous variables are very difficult, and existing algorithms are either computationally intensive or applicable to models with special structure. A new approach for solving nonlinear mixed-discrete problems with no particular structure is presented here, motivated by its efficiency for models with extensive monotonicities of the problem’s objective and constraint functions with respect to the design variables. It involves solving a sequence of mixed-discrete linear approximations of the original nonlinear model. In this article, a review of previous approaches is followed by description of the resulting algorithm, its convergence properties and limitations. Several illustrative examples are given. A sequel article presents a detailed algorithmic implementation and extensive computational results.

Copyright © 1991 by The American Society of Mechanical Engineers
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