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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…
Hidden convex optimization is such a class of nonconvex optimization problems that can be globally solved in polynomial time via equivalent convex programming reformulations. In this paper, we focus on checking local optimality in hidden…
The study of convex functions - in particular, of their optimization (really minimization) is one of the most important fields of applied mathematics. Convexity seems to be one of those incredibly well-chosen hypotheses which is just…
Consider the problem of minimizing a lower semi-continuous semi-algebraic function $f \colon \mathbb{R}^n \to \mathbb{R} \cup \{+\infty\}$ on an unbounded closed semi-algebraic set $S \subset \mathbb{R}^n.$ Employing adequate tools of…
We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
Decision tree optimization is notoriously difficult from a computational perspective but essential for the field of interpretable machine learning. Despite efforts over the past 40 years, only recently have optimization breakthroughs been…
We develop tractable convex relaxations for rank-constrained quadratic optimization problems over $n \times m$ matrices, a setting for which tractable relaxations are typically only available when the objective or constraints admit spectral…
We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
We consider feasibility and constrained optimization problems defined over smooth and/or strongly convex sets. These notions mirror their popular function counterparts but are much less explored in the first-order optimization literature.…
In this article we study optimal control problems for systems that are affine in one part of the control variable. Finitely many equality and inequality constraints on the initial and final values of the state are considered. We investigate…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…
Matrix completion results deal with the question of when a partially specified symmetric matrix can be completed to a member of certain matrix cones. Results from positive semidefinite matrix completion and completely positive matrix…
Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex optimization problems. Within…
Efficient algorithms for convex optimization, such as the ellipsoid method, require an a priori bound on the radius of a ball around the origin guaranteed to contain an optimal solution if one exists. For linear and convex quadratic…
We show that the optimal complexity of Nesterov's smooth first-order optimization algorithm is preserved when the gradient is only computed up to a small, uniformly bounded error. In applications of this method to semidefinite programs,…
In this paper, we study the problem of optimizing a two-layer artificial neural network that best fits a training dataset. We look at this problem in the setting where the number of parameters is greater than the number of sampled points.…