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We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…
Proximal gradient methods are popular in sparse optimization as they are straightforward to implement. Nevertheless, they achieve biased solutions, requiring many iterations to converge. This work addresses these issues through a suitable…
Recently, there has been a surge of research on a class of methods called feedback optimization. These are methods to steer the state of a control system to an equilibrium that arises as the solution of an optimization problem. Despite the…
This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
This paper focuses on optimization problems constrained by Parametric Variational Inequalities (PVI) defined on a moving set. Unlike most existing works on mathematical programs with equilibrium constraints, the equilibrium constraints have…
This paper develops a robust fixed time optimization framework for constrained problems that guarantees exact constraint satisfaction and convergence to KKT points within fixed time , independent of initial conditions. The approach treats…
Ill-posed linear inverse problems appear in many scientific setups, and are typically addressed by solving optimization problems, which are composed of data fidelity and prior terms. Recently, several works have considered a back-projection…
This paper presents a novel factor graph-based approach to solve the discrete-time finite-horizon Linear Quadratic Regulator problem subject to auxiliary linear equality constraints within and across time steps. We represent such optimal…
The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…
In this study, we propose a novel gap-constraint-based reformulation for optimal control problems with equilibrium constraints (OCPECs). We show that the proposed reformulation generates a new constraint system equivalent to the original…
We consider structured optimisation problems defined in terms of the sum of a smooth and convex function, and a proper, l.s.c., convex (typically non-smooth) one in reflexive variable exponent Lebesgue spaces $L_{p(\cdot)}(\Omega)$. Due to…
This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal" +…
Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The…
This paper studies convergence properties of inexact iterative solution schemes for bilevel optimization problems. Bilevel optimization problems emerge in control-aware design optimization, where the system design parameters are optimized…
In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the…
We expose in a tutorial fashion the mechanisms which underlie the synthesis of optimization algorithms based on dynamic integral quadratic constraints. We reveal how these tools from robust control allow to design accelerated gradient…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
This paper studies equality-constrained minimization problems through the lens of feedback control. We introduce a unified control-theoretic framework by showing that a PID feedback law acting on the dual variable induces the PID…