A Simple Method for Solving Nonlinear Non-convex Optimization Problems with Matrix Inequality Constraints with Applications in Structural Optimization
(English)Manuscript (preprint) (Other academic)
This paper is about a simple method for solving nonlinear, non-convex optimization problems (NLPs) with matrix inequality constraints. The method is based on the fact that a symmetric matrix is positive semi-definite if and only if it admits a Cholesky decomposition, and works by reformulating the original matrix inequality constrained problem into a standard NLP, for which there are currently many high-quality codes available. Examples of optimization problems involving matrix inequality constraints are relatively frequent in the structural optimization literature, and to illustrate a potential usage of our method we present numerical solutions for weight minimization of trusses subject to compliance and global buckling constraints. Looking ahead, we also see problems involving simultaneous optimization of both structure and control systems being common, and since matrix inequality constrained problems appear frequently in control theory, we believe that the number of applications for codes like the one presented here will continue to grow rapidly.
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-76983OAI: oai:DiVA.org:liu-76983DiVA: diva2:524024