Noticias en español
Provably efficient high dimensional feature extraction
Abstract: The goal of inference is to extract information from data. A basic building block in high dimensional inference is feature extraction, that is, to compute functionals of given data that represent it in a way that highlights some underlying structure. For example, Principal Component Analysis is an algorithm that finds a basis to represent data that highlights the property of data being close to a low-dimensional subspace. A fundamental challenge in high dimensional inference is the design of algorithms that are provably efficient and accurate as the dimension grows. In this...
Read MoreIterative regularization via a dual diagonal descent method
Abstract: In the context of linear inverse problems, we propose and study general iterative regularization method allowing to consider classes of regularizers and data-fit terms. The algorithm we propose is based on a primal-dual diagonal descent method, designed to solve hierarchical optimization problems. Our analysis establishes convergence as well as stability results, in presence of error in the data. In this noisy case, the number of iterations is shown to act as a regularization parameter, which makes our algorithm an iterative regularization...
Read MoreDoes convexity arise in optimization naturally?
Abstract Convexity is one of the conditions that any researcher may desire to have when dealing with problems in Optimization. Thus, the lack of standard convexity provides an interesting challenge in mathematics. In this talk we show various instances from mathematical programming, differential inclusions to calculus of variations, where convexity is present in one way or in another. Among the issues to be described lie: strong duality, KKT optimality conditions; joint-range and the S-lemma for a pair of (not necessarily homogeneous) quadratic functions; optimal value functions; local...
Read MoreOn the Convergence of Projection Method for Co-coercive Variational Inequalities
Abstract: We revisit the basic projection method for solving co-coercive variational inequalities in real Hilbert spaces. The weak and the strong convergence for the iterative sequences generated by this method are studied. We also propose several examples to analyze the obtained results. This is a joint work with Phan Tu Vuong.
Read MoreNonconvex sweeping processes involving maximal monotone operators
Abstract: By using a regularization method, we study in this paper the global existence and uniqueness property of a new variant of nonconvex sweeping processes involving maximal monotone operators. The system can be considered as a maximal monotone differential inclusion under a control term of normal cone type forcing the trajectory to be always contained in the desired moving set. When the set is fixed, one can show that the unique solution is right-differentiable everywhere and its right-derivative is right-continuous.
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