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Giovanni Bruccola

Publications and source records attributed to Giovanni Bruccola.

6 recordsLinked to original sources
arXiv2026

Global solutions for the sensors placement problem via weakly convex optimization

We address the problem of optimally placing a limited number of sensors to reconstruct high-dimensional signals without knowledge of the underlying dynamics. The task is formulated as a nonconvex combinatorial optimisation problem and recast as a weakly convex constrained projection problem. This reformulation allows us to compute $\varepsilon$-global solutions using the Inexact Cutting Sphere algorithm. We further propose the Inverse Cutting Sphere algorithm, which starts from any feasible heuristic solution and either improves it by a prescribed tolerance $\varepsilon$ or certifies its $\varepsilon$-global optimality. The framework is evaluated on pressure reconstruction for NACA airfoils using XFOIL data.

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arXiv2024

Outer Approximation Scheme for Weakly Convex Constrained Optimization Problems

Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solving variational inequalities, general convex problems, as well as mixed-integer linear, and nonlinear programming problems. In this work, we introduce a novel outer approximation scheme specifically designed for solving weakly convex constrained optimization problems. The key idea lies in utilizing quadratic cuts, rather than the traditional linear cuts, and solving an outer approximation problem at each iteration in the form of a Quadratically Constrained Quadratic Programming (QCQP) problem. The primary result demonstrated in this work is that every convergent subsequence generated by the proposed outer approximation scheme converges to a global minimizer of the general weakly convex optimization problem under consideration. To enhance the practical implementation of this method, we also propose two variants of the algorithm. The efficacy of our approach is illustrated through its application to two distinct problems: the circular packing problem and the Neyman-Pearson classification problem, both of which are reformulated within the framework of weakly convex constrained optimization.

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arXiv2024

Forward-Backward algorithms for weakly convex problems

We investigate the convergence properties of exact and inexact forward-backward algorithms to minimise the sum of two weakly convex functions defined on a Hilbert space, where one has a Lipschitz-continuous gradient. We show that the exact forward-backward algorithm converges strongly to a global solution, provided that the objective function satisfies a sharpness condition. For the inexact forward-backward algorithm, the same condition ensures that the distance from the iterates to the solution set approaches a positive threshold depending on the accuracy level of the proximal computations. As an application of the considered setting, we provide numerical experiments related to discrete tomography.

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arXiv2023

On global solvability of a class of possibly nonconvex QCQP problems in Hilbert spaces

We provide conditions ensuring that the KKT-type conditions characterizes the global optimality for quadratically constrained (possibly nonconvex) quadratic programming QCQP problems in Hilbert spaces. The key property is the convexity of a image-type set related to the functions appearing in the formulation of the problem. The proof of the main result relies on a generalized version of the (Jakubovich) S-Lemma in Hilbert spaces. As an application, we consider the class of QCQP problems with a special form of the quadratic terms of the constraints.

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arXiv2022

Finding global solutions for a class of possibly nonconvex QCQP problems through the S-lemma

In this paper we provide necessary and sufficient (KKT) conditions for global optimality for a new class of possibly nonconvex quadratically constrained quadratic programming (QCQP) problems, denoted by S-QCQP. The class consists of QCQP problems where the matrices of the quadratic components are formed by a scalar times the identity matrix. Our result relies on a generalized version of the S-Lemma, stated in the context of general QCQP problems. Moreover, we prove the exactness of the SDP and the SOCP relaxations for S-QCQP.

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