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Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…

Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…

We consider convex optimization problems formulated using dynamic programming equations. Such problems can be solved using the Dual Dynamic Programming algorithm combined with the Level 1 cut selection strategy or the Territory algorithm to…

In this paper, we address the identification problem for the systems characterized by linear time-invariant dynamics with bilinear observation models. More precisely, we consider a suitable parametric description of the system and formulate…

The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…

Mixed integer convex and nonlinear programs, MICP and MINLP, are expressive but require long solving times. Recent work that combines data-driven methods on solver heuristics has shown potential to overcome this issue allowing for…

Regularized methods have been widely applied to system identification problems without known model structures. This paper proposes an infinite-dimensional sparse learning algorithm based on atomic norm regularization. Atomic norm…

This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…

This paper addresses the problem of recursive set-membership identification for linear time varying (LTV) systems when both input and output measurements are affected by bounded additive noise. First we formulate the problem of online…

The joint optimization of the reconstruction and classification error is a hard non convex problem, especially when a non linear mapping is utilized. In order to overcome this obstacle, a novel optimization strategy is proposed, in which a…

This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…

We introduce a new method to reconstruct unknown quantum states out of incomplete and noisy information. The method is a linear convex optimization problem, therefore with a unique minimum, which can be efficiently solved with Semidefinite…

When solving decision-making problems with mathematical optimization, some constraints or objectives may lack analytic expressions but can be approximated from data. When an approximation is made by neural networks, the underlying problem…

The equivalence of a systematic convolutional encoder as linear state-space control system is first realized and presented through an example. Then, utilizing this structure, a new optimal state-sequence estimator is derived, in the spirit…

We describe a convex programming framework for pose estimation in 2D/3D point-set registration with unknown point correspondences. We give two mixed-integer nonlinear program (MINP) formulations of the 2D/3D registration problem when there…

A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…

This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems that are non-convex in the input norm, which is a…

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…

Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…

Mutual localization is essential for coordination and cooperation in multi-robot systems. Previous works have tackled this problem by assuming available correspondences between measurements and received odometry estimations, which are…