Here we study the integrality properties of singular moduli of a special non-holomorphic function γ(z), which was previously studied by Siegel, Masser, and Bruinier, Sutherland, and Ono. Similar to the modular j-invariant, γ has algebraic values at any CM-point. We show that primes dividing the...
01a Articolo in rivista
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Il lavoro riguarda lo studio di tecniche di machine learning intese come strumento di supporto alle decisioni nella diagnosi del Lupus.
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In this work, we consider the relevant class of Standard Quadratic Programming problems and we propose a simple and quick decomposition algorithm, which sequentially updates, at each iteration, two variables chosen by a suitable selection rule. The main features of the algorithm are the following...
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In this work we present a novel way to solve the sub-problems that originate when using decomposition algorithms to train Support Vector Machines (SVMs). State-of-the-art Sequential Minimization Optimization (SMO) solvers reduce the original problem to a sequence of sub-problems of two variables...
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In this manuscript, we consider the problem of minimizing a smooth function with cardinality constraint, i.e., the constraint requiring that the [InlineEquation not available: see fulltext.]-norm of the vector of variables cannot exceed a given threshold value. A well-known approach of the...
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In the present paper we propose to rewrite a nonsmooth problem subjected to convex constraints as an unconstrained problem. We show that this novel formulation shares the same global and local minima with the original constrained problem. Moreover, the reformulation can be solved with standard...
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The paper is concerned with multiobjective sparse optimization problems, i.e. the problem of simultaneously optimizing several objective functions and where one of these functions is the number of the non-zero components (or the ℓ-norm) of the solution. We propose to deal with the ℓ-norm by means...
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We consider the problem of minimizing a smooth nonconvex function over a structured convex feasible set, that is, defined by two sets of constraints that are easy to treat when considered separately. In order to exploit the structure of the problem, we define an equivalent formulation by...
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In this work we propose a general framework that provides a unified convergence analysis for nonmonotone decomposition algorithms. The main motivation to embed nonmonotone strategies within a decomposition approach lies in the fact that enforcing the reduction of the objective function could be...
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In this work we consider traffic assignment problems with both inelastic and elastic demand. As well-known, the elastic demand problem can be reformulated as a fixed demand problem by a suitable modification of the network representation. Then, the general network equilibrium problem we consider is...