Noticias en español
Iterative 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.
Read MoreVariations of the infimal convolution and application to the minimal time function.
Abstract: We establish in the Banach setting a relationship between the variations of the infimal convolution of a fairly general function and a proper continuous convex function. Namely, we compare the Clarke subdifferential of all these functions at points where the infimal convolution is attained, or strongly attained. This work extends and adapts many of the existing results in the literature. We apply this work to investigate the differentiability of a minimal time function. We also discuss necessary optimality conditions for a location problem.
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