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A Simple Method for Solving Nonlinear Non-convex Optimization Problems with Matrix Inequality Constraints with Applications in Structural Optimization
Linköping University, Department of Management and Engineering, Mechanics. Linköping University, The Institute of Technology.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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.

National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-76983OAI: diva2:524024
Available from: 2012-04-27 Created: 2012-04-27 Last updated: 2012-04-27Bibliographically approved
In thesis
1. Optimal Design of Neuro-Mechanical Networks
Open this publication in new window or tab >>Optimal Design of Neuro-Mechanical Networks
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Many biological and artificial systems are made up from similar, relatively simple elements that interact directly with their nearest neighbors. Despite the simplicity of the individual building blocks, systems of this type, network systems, often display complex behavior — an observation which has inspired disciplines such as artificial neural networks and modular robotics. Network systems have several attractive properties, including distributed functionality, which enables robustness, and the possibility to use the same elements in different configurations. The uniformity of the elements should also facilitate development of efficient methods for system design, or even self-reconfiguration. These properties make it interesting to investigate the idea of constructing mechatronic systems based on networks of simple elements.

This thesis concerns modeling and optimal design of a class of active mechanical network systems referred to as Neuro-Mechanical Networks (NMNs). To make matters concrete, a mathematical model that describes an actuated truss with an artificial recurrent neural network superimposed onto it is developed and used. A typical NMN is likely to consist of a substantial number of elements, making design of NMNs for various tasks a complex undertaking. For this reason, the use of numerical optimization methods in the design process is advocated. Application of such methods is exemplified in four appended papers that describe optimal design of NMNs which should take on static configurations or follow time-varying trajectories given certain input stimuli. The considered optimization problems are nonlinear, non-convex, and potentially large-scale, but numerical results indicate that useful designs can be obtained in practice.

The last paper in the thesis deals with a solution method for optimization problems with matrix inequality constraints. The method described was developed primarily for solving optimization problems stated in some of the other appended papers, but is also applicable to other problems in control theory and structural optimization.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. 42 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1444
National Category
Engineering and Technology
urn:nbn:se:liu:diva-76984 (URN)978-91-7519-900-9 (ISBN)
Public defence
2012-06-01, C3, C-huset, Campus Valla, Linköpings universitet, Linköping, 11:15 (English)
Available from: 2012-04-27 Created: 2012-04-27 Last updated: 2016-03-14Bibliographically approved

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