Diego Regruto

Vito Cerone, Jean-Bernard Lasserre, Dario Piga et al.

In this paper we present a unified framework for solving a general class of problems arising in the context of set-membership estimation/identification theory. More precisely, the paper aims at providing an original approach for the computation of optimal conditional and robust projection estimates in a nonlinear estimation setting where the operator relating the data and the parameter to be estimated is assumed to be a generic multivariate polynomial function and the uncertainties affecting the data are assumed to belong to semialgebraic sets. By noticing that the computation of both the conditional and the robust projection optimal estimators requires the solution to min-max optimization problems that share the same structure, we propose a unified two-stage approach based on semidefinite-relaxation techniques for solving such estimation problems. The key idea of the proposed procedure is to recognize that the optimal functional of the inner optimization problems can be approximated to any desired precision by a multivariate polynomial function by suitably exploiting recently proposed results in the field of parametric optimization. Two simulation examples are reported to show the effectiveness of the proposed approach.

Simone Pirrera, Francesco Ripa, Daniele Astolfi et al.

This paper studies the flows of continuous-time dynamics for equality-constrained optimization based on control-theoretic Lagrangian methods. In particular, we consider dynamics induced by proportional-integral and feedback linearization controllers, which have been recently proposed as alternatives to primal-dual gradient methods. Unlike existing convergence results, which rely on strong convexity of the objective function or boundedness assumptions, we exploit the geometric structure induced by the constraints. Specifically, we show global exponential convergence for non-convex problems that satisfy a suitable convexity property when restricted to the constraint manifold.

Vito Cerone, Sophie M. Fosson, Diego Regruto

The need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm is a valuable method to solve Lasso, which is particularly appreciated for its ease of implementation. Nevertheless, it converges slowly. In this paper, we develop a proximal method, based on logarithmic regularization, which turns out to be an iterative shrinkage-thresholding algorithm with adaptive shrinkage hyperparameter. This adaptivity substantially enhances the trajectory of the algorithm, in a way that yields faster convergence, while keeping the simplicity of the original method. Our contribution is twofold: on the one hand, we derive and analyze the proposed algorithm; on the other hand, we validate its fast convergence via numerical experiments and we discuss the performance with respect to state-of-the-art algorithms.

Vito Cerone, Sophie M. Fosson, Diego Regruto

We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may be present in the feasible set, and the classical l1 approach may be unsuccessful. For this motivation, we propose a non-convex quadratic programming method, which exploits prior information on the magnitude of the non-zero parameters. This results in a more efficient support recovery. We provide sufficient conditions for successful recovery and numerical simulations to illustrate the practical feasibility of the proposed method.