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X-WR-CALDESC:Events for Computational Optimisation Group
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DTSTART:20150101T000000
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BEGIN:VEVENT
DTSTART;TZID=UTC:20161205T150000
DTEND;TZID=UTC:20161205T150000
DTSTAMP:20260419T034540
CREATED:20170116T145614Z
LAST-MODIFIED:20170116T145614Z
UID:428-1480950000-1480950000@optimisation.doc.ic.ac.uk
SUMMARY:Seminar: Solution of an old problem in vector optimisation - Support function of the generalised Jacobian
DESCRIPTION:Title: Solution of an old problem in vector optimisation – Support function of the generalised Jacobian\nSpeaker: Prof. Abbas Edalat\nAffiliation: Department of Computing – Imperial College\nLocation: Room 217 Huxley Building\nTime: 3:00pm (1 hour) \nAbstract. Many optimisation problems are non-smooth in the sense that the objective function is not differentiable. This is invariably the case in many areas of application when the objective function contains simple constructs such as maximum or minimum of several differentiable functions or contains\, for example\, the absolute value function. The notion of the Clarke sub-gradient of locally Lipschitz maps has been used successfully in the past decades to solve non-smooth non-convex optimisation problems by methods such as the sub-gradient descent or the more powerful bundle method. The generalised Jacobian of a locally Lipschitz vector function\, as introduced by Clarke in mid 1970’s\, plays the same role in non-smooth vector (multi-objective) optimisation that the (Clarke) sub-gradient or sub-differential plays in the usual non-smooth scalar optimisation. The sub-gradient of a non-smooth objective function is a non-empty\, compact and convex subset of the finite Euclidean space of the same dimension as the domain of the objective function. Similarly\, the generalised Jacobian is a non-empty\, compact and convex subset of the space of real mxn matrices where n is the dimension of input and m is the dimension of the output of the multi-objective function. However\, until now\, there has been a huge discrepancy in the way they have been defined. The sub-gradient of a scalar function at a point was originally defined constructively by its support function which provides a simple expression for its boundary. In contrast\, the generalised Jacobian has been defined non-constructively by using a theorem of Rademacher in analysis which states that every Lipschitz map between finite dimensional Euclidean spaces is differentiable for almost all its arguments. The non-constructive nature of this definition has created a major obstacle in the application of the generalised Jacobian in vector optimisation and several other fields of computation such as non-smooth Newton method or solution of parametric ODE’s with non-smooth right hand side. There have been two attempts to tackle the problem of finding the support function of the generalised Jacobian. Hiriart-Urruty derived the support function of an approximation to the generalised Jacobian\, namely its so-called plenary hull. Imbert used a Green-Stokes formula to obtain an intractable analytic expression for the support function of the generalized Jacobian that involves a limsup operation over surface integrals of the divergence of the derived function on a shrinking sequence of hypercubes. In this talk\, I will derive a simple expression to compute the support function of the generalised Jacobian after 40 years. It determines the boundary of the non-empty compact convex set that the generalised Jacobian represents in the space of mxn matrices. The derivation is elementary\, does not invoke Rademacher’s theorem and is in the same spirit as that of the sub-gradient of a scalar objective function. Moreover\, I will show that the same technique can be used to compute the generalised Jacobian of locally Lipschitz multi-objective functions defined on an infinite dimensional Banach space\, which allows optimisation over function spaces. \nAbout the speaker. Abbas Edalat has been a professor of computer science and mathematics at the Department of Computing\, Imperial College London\, since 1997.
URL:http://optimisation.doc.ic.ac.uk/event/seminar-solution-of-an-old-problem-in-vector-optimisation-support-function-of-the-generalised-jacobian/
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BEGIN:VEVENT
DTSTART;TZID=UTC:20161206T150000
DTEND;TZID=UTC:20161206T150000
DTSTAMP:20260419T034540
CREATED:20170116T145225Z
LAST-MODIFIED:20170116T145225Z
UID:425-1481036400-1481036400@optimisation.doc.ic.ac.uk
SUMMARY:Seminar: On Bit Representations of Mixed-Integer Quadratic Programs.
DESCRIPTION:Title: On Bit Representations of Mixed-Integer Quadratic Programs.\nSpeaker: Prof. Adam Letchford\nAffiliation: Management School – Lancaster University\nLocation: Room 217 Huxley Building\nTime: 3:00pm (1 hour) \nAbstract. A standard trick in integer programming is to replace each bounded general-integer variable with a small number of binary variables\, using the bit representation of the given variable. (See\, e.g.\, Owen & Mehrotra\, 2002; Coppersmith & Lee\, 2005; Muldoon et al.\, 2013; Bonami & Margot\, 2015). Recently\, bit representation was found to be useful for convexifying quadratic problems (Billionnet et al.\, 2012) and for linearising bilinear problems (Gupte et al.\, 2013). We show that\,in the case of mixed-integer quadratic programs\, bit representation has an additional benefit: it can enable one to obtain stronger linear programming relaxations. \nAbout the speaker. Adam N. Letchford is known internationally for his research on exact solution methods for NP-hard optimisation problems. He has been the recipient of an IBM Faculty Award and an EPSRC Advanced Research Fellowship\, and is a Fellow of the Operational Research Society. He has been on the editorial boards of six journals\, including Mathematical Programming and Operations Research. From 2008-2014\, he was the coordinator of the optimisation cluster of the LANCS Initiative. Since 2012\, he has been the director of NATCOR\, the UK National Taught Course Centre in Operational Research.
URL:http://optimisation.doc.ic.ac.uk/event/seminar-on-bit-representations-of-mixed-integer-quadratic-programs/
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=UTC:20161213T133000
DTEND;TZID=UTC:20161213T133000
DTSTAMP:20260419T034540
CREATED:20170116T144707Z
LAST-MODIFIED:20170116T145403Z
UID:422-1481635800-1481635800@optimisation.doc.ic.ac.uk
SUMMARY:Seminar: Smart Grids and Optimization - A Winning Combination
DESCRIPTION:Title: Smart Grids and Optimization – A Winning Combination\nSpeaker: Prof. Miguel Anjos\nAffiliation: Polytechnique Montreal\nLocation: Room 217 Huxley Building\nTime: 1:30pm (1 hour) \nAbstract. A smart grid is the combination of a traditional electrical power system with information and energy both flowing back and forth between suppliers and consumers. This new paradigm introduces major challenges such as the integration of intermittent generation and storage\, and the need for electricity consumers to play an active role in the operations of the system. We will summarize the opportunities provided by smart grid to the optimization community\, and illustrate one such opportunity through some recent research on optimal aggregation of energy resources (joint work with F. Gilbert\, P. Marcotte\, and G. Savard). \nAbout the speaker. Miguel Anjos is a Professor at Polytechnique Montreal. He holds a Canada Research Chair and an Inria International Chair. He is also a licensed professional engineer in Ontario\, Canada. His research is concerned with using mathematical optimization to provide guaranteed optimal or near-optimal solutions for important classes of large-scale discrete nonlinear optimization problems arising in engineering applications.
URL:http://optimisation.doc.ic.ac.uk/event/seminar-smart-grids-and-optimization-a-winning-combination/
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