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We propose a general approach to directly implement rate constraints on the discretization mesh for all collocation methods, for both state and input variables. Unlike conventional approaches that may lead to singular control arcs, the…
ConArg is a Constraint Programming-based tool that can be used to model and solve different problems related to Abstract Argumentation Frameworks (AFs). To implement this tool we have used JaCoP, a Java library that provides the user with a…
Constraint Programming (CP) has been successfully applied to both constraint satisfaction and constraint optimization problems. A wide variety of specialized global constraints provide critical assistance in achieving a good model that can…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…
This paper compares different exact approaches to solve the Discrete Ordered Median Problem (DOMP). In recent years, DOMP has been formulated using set packing constraints giving rise to one of its most promising formulations. The use of…
This work presents a hybrid approach to solve the maximum stable set problem, using constraint and semidefinite programming. The approach consists of two steps: subproblem generation and subproblem solution. First we rank the variable…
This work concerns the analysis and design of distributed first-order optimization algorithms over time-varying graphs. The goal of such algorithms is to optimize a global function that is the average of local functions using only local…
We provide tight upper and lower bounds on the complexity of minimizing the average of $m$ convex functions using gradient and prox oracles of the component functions. We show a significant gap between the complexity of deterministic vs…
Deep learning models are increasingly deployed in safety-critical tasks where predictions must satisfy hard constraints, such as physical laws, fairness requirements, or safety limits. However, standard architectures lack built-in…
This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…
This article derives lower bounds on the convergence rate of continuous-time gradient-based optimization algorithms. The algorithms are subjected to a time-normalization constraint that avoids a reparametrization of time in order to make…
We describe the use of array expressions as constraints, which represents a consequent generalisation of the "element" constraint. Constraint propagation for array constraints is studied theoretically, and for a set of domain reduction…
We focus on minimizing nonconvex finite-sum functions that typically arise in machine learning problems. In an attempt to solve this problem, the adaptive cubic regularized Newton method has shown its strong global convergence guarantees…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
We revisit the so-called sampling and discarding approach used to quantify the probability of constraint violation of a solution to convex scenario programs when some of the original samples are allowed to be discarded. Motivated by two…
This paper presents a first-order distributed algorithm for solving a convex semi-infinite program (SIP) over a time-varying network. In this setting, the objective function associated with the optimization problem is a summation of a set…
In this paper we consider a general problem set-up for a wide class of convex and robust distributed optimization problems in peer-to-peer networks. In this set-up convex constraint sets are distributed to the network processors who have to…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…