Optimization seminar

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Autumn Semester 2014

Date / Time

Speaker

Title

Location

29 September 2014
16:30-17:30

Prof. Dr. René Henrion
Weierstrass Institute for Applied Analysis and Stochastics, Berlin

Event Details

Optimization Seminar

Title	Probabilistic Constraints: a structure-oriented introduction
Speaker, Affiliation	Prof. Dr. René Henrion, Weierstrass Institute for Applied Analysis and Stochastics, Berlin
Date, Time	29 September 2014, 16:30-17:30
Location	HG G 19.1
Abstract	Probabilistic constraints arise in optimization problems involving inequality constraints which are affected by some random parameter. Typically, a decision has to be taken before the random parameter is observed, so feasibility of a decision in a classical sense is not meaningful. This leads naturally to formulating a so-called probabilistic constraint in which a decision is declared to be feasible whenever the given system of random inequalities is satisfied at least with some probability p under this decision. The principal challenge of such constraints consists in the absence of analytical formulae for function values and gradients. This poses a lot of challenges regarding structural properties (e.g., convexity, continuity, differentiability), stability of solutions (with respect to approximations of the theoretical but generally unknown distribution of the random vector) and algorithmic approaches. The talk aims at a structure-oriented introduction to this topic.

Probabilistic Constraints: a structure-oriented introductionread_more

HG G 19.1

6 October 2014
16:30-17:30

Prof. Dr. Constantin Zalinescu
University "Al. I. Cuza" Iasi, Romania

Event Details

Optimization Seminar

Title	Series of convex functions: subdifferential, conjugate, and applications to entropy maximization
Speaker, Affiliation	Prof. Dr. Constantin Zalinescu, University "Al. I. Cuza" Iasi, Romania
Date, Time	6 October 2014, 16:30-17:30
Location	HG G 19.1
Abstract	X.Y. Zheng (1998) showed, in Banach spaces, that the sub- differential of the sum f of a series of proper convex functions f_n is the sum of the sub- differentials of f_n at any x in the interior D of the domain of f, provided f and f_n are continuous on D. Our aim is to provide a proof for that formula in locally convex spaces under the same conditions on f, f_n and x, and to show that it can be used to obtain a formula for the conjugate of f similar to the one when one has a finite sum of convex functions. However this formula is valid only for elements in the image of D by the subdifferential of f. We then show how the mentioned results can be used to obtain rigorously the maximum of the Boltzmann entropy for some classical choices of level energies, as well as the corresponding Boltzmann distribution.

Series of convex functions: subdifferential, conjugate, and applications to entropy maximizationread_more

HG G 19.1

20 October 2014
16:30-17:30

Prof. Dr. Neil Walton
University of Amsterdam, The Netherlands

Event Details

Optimization Seminar

Title	Efficient Advert Assignment
Speaker, Affiliation	Prof. Dr. Neil Walton, University of Amsterdam, The Netherlands
Date, Time	20 October 2014, 16:30-17:30
Location	HG G 19.1
Abstract	We develop a framework for the analysis of large-scale Ad-auctions where adverts are assigned over a continuum of search types. For this pay-per-click market, we provide an efficient and highly decomposed mechanism that maximizes social welfare. In particular, we show that the social welfare optimization can be solved in separate optimizations conducted on the time-scales relevant to the advertisement platform and advertisers. Here, on each search occurrence, the platform solves an assignment problem and, on a slower time scale, each advertiser submits a bid which matches its demand for click-throughs with supply. Importantly knowledge of global parameters, such as the distribution of search terms, is not required when separating the problem in this way. This decomposition is implemented in an adversarial setting. Exploiting the information asymmetry between the platform and advertiser, we describe a simple mechanism which incentivizes truthful bidding and has a unique Nash equilibrium that is socially optimal, and thus implements our decomposition. Further, we consider models where advertisers adapt their bids smoothly over time, and prove convergence to the solution that maximizes aggregate utility. Finally, we describe several extensions which illustrate the flexibility and tractability of our framework. (This is joint work with Frank Kelly, Uni. of Cambridge, and Peter Key, Microsoft Research)

Efficient Advert Assignmentread_more

HG G 19.1

3 November 2014
16:30-17:30

Prof. Dr. Matthias Koeppe
University of California, Davis, USA

Event Details

Optimization Seminar

Title	Light on the infinite group relaxation
Speaker, Affiliation	Prof. Dr. Matthias Koeppe, University of California, Davis, USA
Date, Time	3 November 2014, 16:30-17:30
Location	HG G 19.1
Abstract	The infinite group problem was introduced 42 years ago by Ralph Gomory and Ellis Johnson in their groundbreaking papers titled "Some continuous functions related to corner polyhedra I, II". The technique, investigating strong relaxations of integer linear programs by convexity in a function space, has often been dismissed as "esoteric". Now we recognize the infinite group problem as a technique which was decades ahead of its time, and which may be the key to today's pressing need for stronger, "multi-row" cutting plane approaches. We survey the recent progress on the problem, present software, and highlight a related open algorithmic-algebraic problem, the effective computation of the "moves semigroup". (based on joint work with A. Basu, R. Hildebrand, R. La Haye, M. Molinaro, Q. Louveaux, Y. Zhou)

Light on the infinite group relaxationread_more

HG G 19.1

24 November 2014
16:30-17:30

Prof. Dr. Nikolas Geroliminis
EPF Lausanne

Event Details

Optimization Seminar

Title	A hierarchical control approach for large-scale traffic networks
Speaker, Affiliation	Prof. Dr. Nikolas Geroliminis, EPF Lausanne
Date, Time	24 November 2014, 16:30-17:30
Location	HG G 19.2
Abstract	As cities around the world grow rapidly and more people through different modes compete for limited urban road infrastructure to travel, it is important to this space can be manage this space to improve accessibility for travelers. This research targets to operate traffic in future cities in a holistic way that was not possible until now. It tackles the problem of modeling and optimization in large-scale congested traffic networks with an aggregated realistic representation of traffic dynamics and route choice and multiple modes of transport. Mobility advances through the integration of big data, the understanding of multimodal patterns, the coordination and optimization of urban efficiency and sustainability for the travel of people and goods. This is challenging because cities are highly complex systems. This seminar will describe methodologies to model and understand the collective behavior for different types of urban systems. It will highlight under what physical properties the aggregated laws will provide reasonable description of congestion for single- and multi-modal systems. Ultimately, the goal is to develop optimization tools and investigate what type of real-time active traffic management schemes (congestion pricing, vehicle restriction, large scale traffic signal control) can improve mobility measures in a city for cities of different structures. We build a hierarchical feedback control network of multiple levels. The validation of the modeling methodologies and the traffic management schemes are conducted in various and complex city structures scenarios using data from field experiments and micro-simulations.

A hierarchical control approach for large-scale traffic networksread_more

HG G 19.2

8 December 2014
16:30-17:30

Prof. Dr. Jiri Outrata
Czech Academy of Sciences, Prague

Event Details

Optimization Seminar

Title	On Walras-Cournot-Nash equilibria and their computation
Speaker, Affiliation	Prof. Dr. Jiri Outrata, Czech Academy of Sciences, Prague
Date, Time	8 December 2014, 16:30-17:30
Location	HG G 19.1
Abstract	The talk is devoted to a class of hierarchical games with the Walras equilibrium on the upper and the Nash (Cournot-Nash) equilibrium on the lower level. This model has been suggested by S.D.Flaam for modelling oligopolistic markets with a rare resource, whose allocation among the agents is provided by an outer authority. Under reasonable assumptions we prove the existence of this equilibrium and propose a numerical approach for its computation. This approach is based on a reformulation of this game as a "mathematical program with equilibrium constraints" which is then solved via a variant of the Implicit programming approach. Illustrative numerical examples are provided.

On Walras-Cournot-Nash equilibria and their computationread_more

HG G 19.1

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Organizers: Bernd Gärtner, Diethard Klatte, John Lygeros, Manfred Morari, Karl Schmedders, Roy Smith, Robert Weismantel, Rico Zenklusen

Archive: SS 22 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11 SS 11 AS 10 SS 10 AS 09