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X-WR-CALDESC:Events for Computational Optimisation Group
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DTSTART:20140101T000000
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BEGIN:VEVENT
DTSTART;TZID=UTC:20150204T140000
DTEND;TZID=UTC:20150204T140000
DTSTAMP:20260511T052600
CREATED:20170124T102138Z
LAST-MODIFIED:20170124T102138Z
UID:563-1423058400-1423058400@optimisation.doc.ic.ac.uk
SUMMARY:Seminar: Bayesian Optimization
DESCRIPTION:Title: Bayesian Optimization Speaker: Dr. Mike OsborneAffiliation: Department of Engineering Science – University of Oxford Location: Room 145 HuxleyTime: 2:00pm \nAbstract.  \nAbout the speaker.
URL:http://optimisation.doc.ic.ac.uk/event/seminar-bayesian-optimization/
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BEGIN:VEVENT
DTSTART;TZID=UTC:20150206T150000
DTEND;TZID=UTC:20150206T150000
DTSTAMP:20260511T052600
CREATED:20170124T102138Z
LAST-MODIFIED:20170124T102138Z
UID:562-1423234800-1423234800@optimisation.doc.ic.ac.uk
SUMMARY:Seminar: McCormick Relaxations: Convergence Rate and Extension to Multivariate Outer Functions
DESCRIPTION:Title: McCormick Relaxations: Convergence Rate and Extension to Multivariate Outer FunctionsSpeaker: Prof. Alexander MitsosAffiliation: Laboratory for Process Systems Engineering – RWTH Aachen UniversityLocation: CPSE seminar room (C615 Roderic Hill)Time: 3:00pm \nAbstract. Optimization is a widely used tool in process systems engineering\, but often the optimization problems have multiple suboptimal local minima. Deterministic global optimization algorithms can solve such problems\, typically employing convex/concave relaxations of the objective and constraints. Several methods have been proposed for the construction of convergent relaxations\, including the McCormick relaxations. These provide the framework for the computation of convex relaxations of composite functions. McCormick’s relaxations are clearly a very important tool\, but they have the limitation of only allowing univariate composition. Although most functions can be decomposed in a way that only univariate functions are used as building blocks\, this often results in weak relaxations. Moreover\, McCormick has not provided results for the convergence rate of these relaxations. We propose a reformulation of McCormick’s composition theorem\, which while equivalent to the original\, suggests a straight forward generalization to multi-variate outer functions. In addition to extending the framework\, the multi-variate McCormick relaxation is a useful tool for the proof of relaxations: by direct application to the product\, division and minimum/maximum of two functions\, we obtain improved relaxations when comparing with uni-variate McCormick. Furthermore\, we generalize the theory for the computation of subgradients to the multi-variate case\, envisioning practical methods that utilize the framework. Further\, we extend the notion of convergence order from interval extensions to convex relaxations in the pointwise metric and Hausdorff metric. We develop theory for the McCormick relaxations by establishing convergence rules for the addition\, multiplication and composition operations. The convergence order of the composite function depends on the convergence order of the relaxations of the factors. No improvement in the order of convergence compared to that of the underlying bound calculation\, e.g.\, via interval extensions\, can be guaranteed unless the relaxations of the factors have pointwise convergence of high order\, in which case at least quadratic conver- gence order can be guaranteed. Additionally\, the McCormick relaxations are compared with the alphaBB relaxations by Floudas and coworkers\, which also guarantee quadratic pointwise convergence. Finally\, the convergence order of McCormick-Taylor models is addressed. Illustrative and numerical examples are given and hybrid methods are discussed. The implication of the results are discussed for practical bound calculations as well as for convex/concave relaxations of factors commonly found in process systems engineering models. \nAbout the speaker. Alexander Mitsos is a Full Professor (W3) in RWTH Aachen University\, and the Director of the Laboratory for Process Systems Engineering (AVT.SVT)\, comprising 40 research and administrative staff. Mitsos received his Dipl-Ing from University of Karlsruhe in 1999 and his Ph.D.  from MIT in 2006\, both in Chemical Engineering. Prior appointments include military service\, free-lance engineering\, involvement in a start-up company\, a junior research group leader position in the Aachen Institute of Computational Engineering Science and the Rockwell International Assistant Professorship at MIT. Mitsos has over 60 publications in peer-reviewed journals and has received a number of awards. His research focuses on optimization of energy and chemical systems and development of enabling numerical algorithms.
URL:http://optimisation.doc.ic.ac.uk/event/seminar-mccormick-relaxations-convergence-rate-and-extension-to-multivariate-outer-functions/
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BEGIN:VEVENT
DTSTART;TZID=UTC:20150211T110000
DTEND;TZID=UTC:20150211T110000
DTSTAMP:20260511T052600
CREATED:20170124T102138Z
LAST-MODIFIED:20170124T102138Z
UID:561-1423652400-1423652400@optimisation.doc.ic.ac.uk
SUMMARY:Seminar: Worst-case complexity of nonlinear optimization: Where do we stand?
DESCRIPTION:Title: Worst-case complexity of nonlinear optimization: Where do we stand?Speaker: Prof. Philippe TointAffiliation: Department of Mathematics – Université de NamurLocation: CPSE seminar room (C615 Roderic Hill)Time: 11:00am \nAbstract. We review the available results on the evaluation complexity of algorithms using Lipschitz-continuous Hessians for the approximate solution of nonlinear and potentially nonconvex optimization problems. Here\, evaluation complexity is a bound on the largest number of problem functions (objective\, constraints) and derivatives evaluations that are needed before an approximate first-order critical point of the problem is guaranteed to be found. We start by considering the unconstrained case and examine classical methods (such as Newton’s method) and the more recent ARC2 method\, which we show is optimal under reasonable assumptions. We then turn to constrained problems and analyze the case of convex constraints first\, showing that a suitable adaptation ARC2CC of the ARC2 approach also possesses remarkable complexity properties. We finally extend the results obtained in simpler settings to the general equality and inequality constrained nonlinear optimization problem by constructing a suitable ARC2GC algorithm whose evaluation complexity also exhibits the same remarkable properties. \nAbout the speaker. Philippe L. Toint (born 1952) received its degree in Mathematics in the University of Namur (Belgium) in 1974 and his Ph.D. in 1978 under the guidance of Prof M.J.D. Powell. He was appointed as lecturer at the University of Namur in 1979 were he became associate professor in 1987 and full-professor in 1993. Since 1979\, he has been the co-director of the Numerical Analysis Unit and director of the Transportation Research Group in this department. He was in charge of the University Computer Services from 1998 to 2000 and director of the Department of Mathematics from 2006 to 2009. He currently serves as Vice-rector for Research and IT for the university. His research interests include numerical optimization\, numerical analysis and transportation research. He has published four books and more than 280 papers and technical reports. Elected as SIAM Fellow (2009)\, he was also awarded the Beale-Orchard-Hayes Prize (1994\, with Conn and Gould)) and the Lagrange Prize in Continuous Optimization (2006\, with Fletcher and Leyffer). He is the past Chairman (2010-2013) of the Mathematical Programming Society\, the international scientific body gathering most researchers in mathematical optimization world-wide. Married and father of two girls\, he is a keen music and poetry lover as well as an enthusiast scuba-diver.
URL:http://optimisation.doc.ic.ac.uk/event/seminar-worst-case-complexity-of-nonlinear-optimization-where-do-we-stand/
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