## PGMO Seminars 2014

**16 Décembre 2014 **

**Youcef Sahraoui**(EDF R&D / LIX) "Dealing with real-world data and modelling of a short-term hydro-power unit-commitment problem"

**Raouia Taktak**(LIX) "Short-term Unit Commitment Problem in Hydro Valleys: Overview and Reformulations"

**29 Septembre 2014**

**Andrzej Ruszczynski**(Rutgers University) Dynamic Risk-Averse Optimization

In the first part of the talk we shall present main ideas of risk modeling in decision problems under uncertainty: utility functions, mean--risk models, measures of risk and stochastic dominance. We shall discuss their relations and their use in optimization problems. We shall then focus on main questions of modeling risk in dynamical systems and discuss the property of time consistency and the resulting interchangeability in optimization models.

In the second part of the talk we shall discuss risk-averse dynamic optimization models and corresponding solution methods. Special attention will be paid to models of risk-averse control of Markov systems. We shall refine the concept of time-consistency for these models and introduce Markov risk measures. We shall develop dynamic programming equations, review solution methods, and present some examples.

**4 Août 2014**

**Jesús Antonio De Loera**(University of California at Davis) "Integral versions of Helly's theorem and Applications to Optimization"

The famous Doignon-Bell-Scarf theorem is a Helly-type result about the existence of integer solutions on systems linear inequalities. The purpose of this paper is to present the following "weighted'' generalization: Given an integer k, we prove that there exists a constant c(k,n), depending only on the dimension n and k, such that if a polyhedron {x : Ax b} contains exactly k integer solutions, then there exists a subset of the rows of cardinality no more than c(k,n), defining a polyhedron that contains exactly the same k integer solutions. We work on both upper and lower bounds for this constant.

**Shinji Mizuno**(Tokyo Institute of Technology) "The LP-Newton method for standard form linear programming problems"

Fujishige et al. propose the LP-Newton method, a new algorithm for solving linear programming problems (LPs). They address LPs which have a lower and an upper bound for each variable. They reformulate the problem by introducing a related zonotope. Their algorithm solves the problem by repeating projections to the zonotope. In this paper, we develop the LP-Newton method for solving standard form LPs. We recast the LP by introducing a related convex cone. Our algorithm solves the problem by iterating projections to the convex cone.

**12 Juin 2014**

- J
**on LEE**(U. Michigan) "Two stories of matrix optimization"

**Marcia FAMPA**(Universidade Federal de Rio de Janeiro) "Formulations and solution approaches for the Euclidean Steiner Problem in-n-space"

**22 Mai 2014**

**Mickael POSS**(Heudiasyc, CNRS) "Optimisation robuste ajustable, applications dans la conception de réseaux"

**5 - 6 Mai 2014**

**Georg PFLUG**(University of Vienna) "Multistage stochastic optimization : approximations, bouds and time consistency"

"Quite often, the result of our decisions depend on the action of others. A typical example is the setting of contracts, where the price is set by one party and the way how the contract is executed is decided by another party. These are examples of hierarchical leader-follower games of the Stackelberg type. We introduce stochastic Stackelberg games and demonstrate their complexity. Necessary optmality conditions are presented. A particular difficulty is due to the fact that even in linear situations the upper level feasible set may be non convex and disconnected. In particular, flexible electricity delivery contracts, called swing options are considered. In this case we are able to use a specially taylored a solution algorithm. since the upper level problem is univariate. We give examples and show numerical results."

**10 Avril 2014**

**Matthieu Kowalski**(Université Paris-sud) "Inverse problems: a sparse synthesis approach"

We consider several example linear inverse problems such as M/EEG sources localization, source séparation or audio signal restauration, and how the sparse principle together with a synthesis approach of the signals can be used for their inversions. We look at how the signals can be constructed using waveforms, such as a time-frequency dictionary, i.e. find the coefficient in their linear combination. We show how this point of view allows the easy introduction of prior information into the representation. We give an overview over methods for

transform domain modeling, in particular those based on sparsity andstructured sparsity. These methods are mainly build over convex optimization approaches and iterative thresholding algorithms .

**Nicolas Chauffert**(CEA) "From compressed sensing to realistic sampling: the example of MRI"

Reducing acquisition time is a crucial challenge for many imaging techniques. Compressed Sensing (CS) theory offers an appealing framework to address this issue since it provides theoretical guarantees on the reconstruction of sparse signals by projection on a low dimensional linear subspace. Unfortunately, standard CS sample selection is based on independent drawings, yielding sampling schemes non implementable on actual devices. For example, in Magnetic Resonance Imaging (MRI), undersampling is perfomed by continuous trajectories, such as radial lines, or spiral.

In this talk, we propose a definition of Variable density sampling, which encompasses CS acquisitions and most of classical continuous sampling approaches. Through original examples, we illustrate the key properties of a VDS to be accounted for in order to design optimal sampling trajectories in MRI, namely the limit of the empirical measure and the ability to cover the acquisition space as fast as possible.

**13 Février 2014**

**Immanuel Bomze**(University of Vienna) "Copositive relaxation beats Lagrangian dual bounds in quadratically and linearly constrained QPs"

**Abdel Lisser**(LRI, Université d'Orsay) "Joint probabilistic constraints"