NDLI: On convexification of some minimum distance problems

Content Provider	IEEE Xplore Digital Library
Author	Chesi, G. Tesi, A. Vicino, A. Genesio, R.
Copyright Year	1999
Description	Author affiliation: Dipt. di Sist. e Inf., Univ. di Firenze, Florence, Italy (Tesi, A.; Genesio, R.) \|\| Dipt. di Ing. dell'Inf., Univ. di Siena, Siena, Italy (Chesi, G.; Vicino, A.)
Abstract	This paper considers the problem of determining the minimum euclidean distance of a point from a polynomial surface in $R^{n}.$ It is well known that this problem is in general non-convex. The main purpose of the paper is to investigate to what extent Linear Matrix Inequality (LMI) techniques can be exploited for solving this problem. The first result of the paper shows that a lower bound to the global minimum can be achieved via the solution of a one-parameter family of Linear Matrix Inequalities (LMIs). It is also pointed out that for some classes of problems the solution of a single LMI problem provides the lower bound. The second result concerns the tightness of the bound. It is shown that optimality of the lower bound can be easily checked via the solution of a system of linear equations. Two application examples are finally presented to show potentialities of the approach.
Starting Page	1446
Ending Page	1451
File Size	284518
Page Count	6
File Format	PDF
ISBN	9783952417355
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1999-08-31
Publisher Place	Germany
Access Restriction	Subscribed
Rights Holder	EUCA
Subject Keyword	Symmetric matrices Homogeneous form Stability Control systems Polynomials Convex functions Eigenvalues and eigenfunctions Robustness Linear matrix inequalities Optimization Linear Matrix Inequalities (LMIs)
Content Type	Text
Resource Type	Article

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