Solutions and optimality criteria to box constrained nonconvex minimization problems

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Date
2007-05-01
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Volume Title
Publisher
American Institute of Mathematical Sciences
Abstract

The design of elastic structures to optimize strength and economy of materials is a fundamental problem in structural engineering and related areas of applied mathematics. In this article we explore a finite dimensional framework for approximate solution of such design problems based on linear elasticity with a range of elastic coefficients assumed available as design parameters. Solution methods for related optimization problems based on the matrix trace norm are suggested and analyzed, providing existence and uniqueness theorems. Results of computations for sample problems are presented and compared with parallel results in the literature based on other approaches.

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Keywords
Structural optimization, Linear elastic systems, Convex programming, Gradient projection method, Constraints, Mathematics, applied, Mathematics
Citation
Gao, D. Y., "Solutions and optimality criteria to box constrained nonconvex minimization problems," J. Industrial and Management Optimization 3(2), 293-304, (2007); DOI: 10.3934/cpaa.2011.10.1517