Related papers: Improving Fast Dual Ascent for MPC - Part II: The …
In dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main…
In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…
A conventional way to handle model predictive control (MPC) problems distributedly is to solve them via dual decomposition and gradient ascent. However, at each time-step, it might not be feasible to wait for the dual algorithm to converge.…
We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
Ill-posed inverse problems are fundamental in many domains, ranging from astrophysics to medical imaging. Emerging diffusion models provide a powerful prior for solving these problems. Existing maximum-a-posteriori (MAP) or posterior…
We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
Dual ascent (DA) and the method of multipliers (MM) are fundamental methods for solving linear equality-constrained convex optimization problems, and their dual updates can be viewed as the minimization of a proximal linear surrogate…
This Ph.D. dissertation contains results in two different but related fields: the implementation of model predictive control (MPC) in embedded systems using first order methods, and restart schemes for accelerated first order methods…
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical…
Model Predictive Control (MPC) for tracking formulation presents numerous advantages compared to standard MPC, such as a larger domain of attraction and recursive feasibility even when abrupt changes in the reference are produced. As a…
Primal-Dual Hybrid Gradient (PDHG) and Alternating Direction Method of Multipliers (ADMM) are two widely-used first-order optimization methods. They reduce a difficult problem to simple subproblems, so they are easy to implement and have…
We propose $\textsf{ScaledGD($\lambda$)}$, a preconditioned gradient descent method to tackle the low-rank matrix sensing problem when the true rank is unknown, and when the matrix is possibly ill-conditioned. Using overparametrized factor…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
Recently there has been an increasing interest in primal-dual methods for model predictive control (MPC), which require minimizing the (augmented) Lagrangian at each iteration. We propose a novel first order primal-dual method, termed…
The recent promises of Model Predictive Control in robotics have motivated the development of tailored second-order methods to solve optimal control problems efficiently. While those methods benefit from strong convergence properties,…
The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…
This paper investigates the collision-free control problem for multi-agent systems. For such multi-agent systems, it is the typical situation where conventional methods using either the usual centralized model predictive control (MPC), or…