Optimization and Control Seminar, Spring 2008
| Thursday, March 6, 2008, 11:00-12:00 |
SOND 406 |
| Higher order corrector-predictor infeasible interior point method for sufficient linear complementarity problems |
| - Mr. Adrian Vancea |
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| Abstract: I will present a corrector-predictor method for solving sufficient
linear complementarity problems (LCP) with an infeasible starting point. The
method generates a sequence of iterates in an $l_2$-neighborhood of the
infeasible central path of the LCP without depending on the handicap
$\kappa$ of the problem, so it may be used for any sufficient linear
complementarity problem. Our algorithm has the best known iteration
complexity if the starting point is feasible or close to be feasible and
also if our starting point is "big enough". Moreover, our algorithm is
superlinearly convergent even for degenerate problems. More precisely, by
using a predictor with order $m>1$, we show that the duality gap converges
to zero with Q-order $m+1$ in the nondegenerate case, and with Q-order
$(m+1)/2$ in the degenerate case. Some numerical results are given to
demonstrate this method's effectiveness.
Note: This is a joint work with: Dr. Potra, C. Petra, F. Gurtuna and O.
Schevchenko
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| Thursday, March 13, 2008, 12:00-1:00 pm |
SOND 406 |
| Positive Invariance of Constrained Affine Dynamics and Its Applications to Hybrid Systems and Safety Analysis |
| - Dr. Jinglai Shen |
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| Abstract: This talk is the first part of a series of two talks on global long-time behaviors of constrained affine dynamics, motivated by recent work on piecewise affine systems (PASs) and reachability analysis of linear/affine dynamics. We will start with a brief review of local and
finite-time switching properties of (Lispchitz continuous) PASs, for
example, non-Zenoness and simple switching behavior, and discuss their
applications to dynamical complementarity systems. We then focus on global
long-time switching behaviors of PASs. We show that the positively invariant
set associated with each affine dynamics plays an important role in
characterization of various global switching dynamics of PASs. We will
discuss certain properties of positively invariant sets and their
implications to PASs and reachability analysis.
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| Thursday, March 27, 2008, 12:00-1:00 pm |
SOND 406 |
| Some inertia theorems in Euclidean Jordan algebras |
| - Dr. Jiyuan Tao of Loyola College |
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| Abstract: In this talk we present some inertia theorems in Euclidean Jordan algebras. First, based on the continuity of eigenvalues, we give an alternate proof of Kaneyuki's generalization of
Sylvester's law of inertia in simple Euclidean Jordan algebras. As a
consequence, we show that the cone spectrum of any quadratic representation
with respect to a symmetric cone is finite. Second, we present
Ostrowski-Schneider type inertia results in Euclidean Jordan algebras. In
particular, we relate the inertias of objects $a$ and $x$ in a Euclidean
Jordan algebra when $L_a(x)>0$ or $S_a(x)>0$, where $L_a$ and $S_a$ denote
Lyapunov and Stein transformations respectively.
This is a joint work with M.S. Gowda and M. Moldovan.
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| Thursday, April 3, 2008, 12:00-1:00 pm |
SOND 406 |
| Some inertia theorems in Euclidean Jordan algebras |
| - Dr. Jiyuan Tao of Loyola College |
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| Abstract: This talk will be continuity of the last week talk, we present Ostrowski-Schneider type inertia results in Euclidean Jordan algebras. In particular, we relate the inertias of
objects $a$ and $x$ in a Euclidean Jordan algebra when $L_a(x)>0$ or
$S_a(x)>0$, where $L_a$ and $S_a$ denote Lyapunov and Stein transformations
respectively.
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| Thursday, April 10, 2008, 12:00-1:00 pm |
SOND 406 |
| Duality of ellipsoidal approximations via semi-infinite programming |
| - Ms. Filiz Gurtuna of UMBC |
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| Abstract: Finding the minimum volume ellipsoid containing a convex body
and the maximum volume ellipsoid contained in a convex body are very
important problems having applications in optimization, statistics, data
mining and control theory, among others. As the numerical computation of
these ellipsoids is needed in all the applications mentioned, the study of
the dual problems becomes crucial. In this work, we develop duality of the
minimum volume circumscribed ellipsoid and the maximum volume inscribed
ellipsoid problems. We present a unified treatment of both problems using
convex semi--infinite programming. We establish the known duality
relationship between the minimum volume circumscribed ellipsoid problem
and the optimal experimental design problem in statistics. The duality
results are obtained utilizing (in fact, developing) convex duality for
semi--infinite programming in a functional analysis setting.
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