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Prochains exposés

SPOT 91 – Lundi 9 septembre 2024

14h : Guoyin Li (The University of New South Wales, Sydney, Australia)

Proximal methods for nonsmooth and nonconvex fractional programs: when sparse optimization meets fractional programs

Nonsmooth and nonconvex fractional programs are ubiquitous and also highly challenging. It includes the composite optimization problemsstudied extensively lately, and encompasses many important modern optimization problems arising from diverse areas such as the recent proposed scale invariant sparse signal reconstruction problem in signal processing, the robust Sharpe ratio optimization problems in finance and the sparse generalized eigenvalue problem in discrimination analysis. In this talk, we will introduce extrapolated proximal methods for solving nonsmooth and nonconvex fractional programs and analyse their convergence behaviour. Interestingly, we will show that the proposed algorithm exhibits linear convergence for the scale invariant sparse signal reconstruction model, and the sparse generalized eigenvalue problem with either cardinality regularization or sparsity constraints. This is achieved by identifying the explicit desingularization function of the Kurdyka-Lojasiewicz inequality for the merit function of the fractional optimization models. Finally, if time permits, we will present some preliminary encouraging numerical results for the proposed methods for sparse signal reconstruction and sparse Fisher discriminant analysis.

The talk is Based on joint work with R.I. Boţ, M. Dao, T.K. Pong and P. Yu.

15h – Marouan Handa (Czech Technical University in Prague and Czech Academy of Sciences, Prague)

Design of frame structures with term sparse polynomial optimization

In this talk, we focus on two fundamental problems in topology optimization of frame structures. The first one involves minimizing structural compliance under linear-elastic equilibrium and weight constraint, while the second one minimizes the weight under compliance constraints. In order to capture the bending-resistant effect, one has to model the stiffness matrix, involved in the linear-elastic equilibrium, as a polynomial of the cross-sections areas. Thus, the resulting optimization problems are non-convex and generally challenging to solve globally. In this presentation, we show that these problems, after appropriate reformulations, can be tackled using the moment-sum-of-squares (mSOS) hierarchy. Moreover, we improve the scalability of the solutions by using the mSOS hierarchy supplemented with the Term Sparsity Pattern (TSP) technique. Due to the unique polynomial structure of our problems in which the objective and constraint functions are separable polynomials, we further improve scalability by adopting a reduced monomial basis containing non-mixed terms only.

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Comité local d’organisation

Une séance par mois environ, avec deux conférenciers chaque fois (deux conférences de type différent : une orientée fondements et une orientée applications, un conférencier de l’environnement toulousain et un conférencier extérieur, un conférencier du milieu académique et un conférencier du milieu de l’industrie et des services, etc.).

Horaire habituel : le lundi après-midi de 14h à 16h.

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Lieu

Sauf indication contraire, à la salle des thèses (C002) à l’ENSEEIHT (N7), 2 rue Charles Camichel, 31000 Toulouse  (métro B, François Verdier). Attention, présentez-vous au poste de garde afin d’accéder au site.

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