VILLA , Silvia

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Let us consider the set of lower semicontinuous functions defined on a Banach space, equipped with the AW-convergence. A function is called Tikhonov well-posed provided it has a unique minimizer to which every minimizing sequence converges. We show that well-posedness of f guarantees strong convergence of approximate minimizers of τaw...

We find a sufficient condition guaranteeing well-posedness in a strong sense of the minimization of a multiple integral on the Sobolev space W 1,1 (Ω Rm) with boundary datum equal to zero. We remark that this condition does not involve global convexity of the integrand and therefore it allows us to find well-posedness properties of two classes...

We find a sufficient condition which does not involve global convexity, guaranteeing well-posedness in a strong sense of the minimization of a multiple integral on the Sobolev space W1,1(Ω ℝm) with boundary datum equal to zero. In particular we apply our result to some nonconvex problems recently studied: functionals depending only on the...

Approximability of sliding motions for control systems governed by nonlinear finite-dimensional differential equations is considered. This regularity property is shown to be equivalent to Tikhonov well-posedness of a related minimization problem in the context of relaxed controls. This allows the derivation of a general approximability result,...

Approximability of sliding motions for control systems governed by nonlinear finite-dimensional differential equations is considered. This regularity property is shown to be equivalent to Tikhonov well-posed ness of a related minimisation problem in the context of relaxed controls. This allows us to give a general approximability result, which...

We consider the following pair of linear programming problems in duality: parameterized by the m × n matrix A defining the inequality constraints. The main result of the paper states that in the case m ≥ n the set S of well posed problems in a very strong sense is a generic subset of the set of problems having solution. Generic here means that...

Multi-task learning is a natural approach for computer vision applications that require the simultaneous solution of several distinct but related problems, e.g. object detection, classification, tracking of multiple agents, or denoising, to name a few. The key idea is that exploring task relatedness (structure) can lead to improved...

We study the l(1) regularized least squares optimization problem in a separable Hilbert space. We show that the iterative soft-thresholding algorithm (ISTA) converges linearly, without making any assumption on the linear operator into play or on the problem. The result is obtained combining two key concepts: the notion of extended support, a...

We propose an inertial forward–backward splitting algorithm to compute a zero of a sum of two monotone operators allowing for stochastic errors in the computation of the operators. More precisely, we establish almost sure convergence in real Hilbert spaces of the sequence of iterates to an optimal solution. Then, based on this analysis, we...