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In this paper, we develop an interior-point method for solving a class of convex optimization problems with time-varying objective and constraint functions. Using log-barrier penalty functions, we propose a continuous-time dynamical system…
Randomized optimization is an established tool for control design with modulated robustness. While for uncertain convex programs there exist randomized approaches with efficient sampling, this is not the case for non-convex problems.…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
In this paper, we consider the minimization of a nonsmooth nonconvex objective function $f(x)$ over a closed convex subset $\mathcal{X}$ of $\mathbb{R}^n$, with additional nonsmooth nonconvex constraints $c(x) = 0$. We develop a unified…
We show how the solution to NMPC problems for a special type of input-affine discrete-time systems can be obtained by reformulating the underlying non-convex optimal control problem in terms of a finite number of convex subproblems. The…
The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand. We reduce the complexity of algorithm design for…
In this paper, we study the use of state-of-the-art nonlinear system identification techniques for the optimal control of nonlinear systems. We show that the nonlinear systems identification problem is equivalent to estimating the…
We develop an indirect-adaptive model predictive control algorithm for uncertain linear systems subject to constraints. The system is modeled as a polytopic linear parameter varying system where the convex combination vector is constant but…
This paper explores the role of regularization in data-driven predictive control (DDPC) through the lens of convex relaxation. Using a bi-level optimization framework, we model system identification as an inner problem and predictive…
Many techniques for online optimization problems involve making decisions based solely on presently available information: fewer works take advantage of potential predictions. In this paper, we discuss the problem of online convex…
We study how to safely control nonlinear control-affine systems that are corrupted with bounded non-stochastic noise, i.e., noise that is unknown a priori and that is not necessarily governed by a stochastic model. We focus on safety…
Decentralized optimization strategies are helpful for various applications, from networked estimation to distributed machine learning. This paper studies finite-sum minimization problems described over a network of nodes and proposes a…
In this paper, we generalize the chance optimization problems and introduce constrained volume optimization where enables us to obtain convex formulation for challenging problems in systems and control. We show that many different problems…
Solving optimal control problems (OCPs) of autonomous agents operating under spatial and temporal constraints fast and accurately is essential in applications ranging from eco-driving of autonomous vehicles to quadrotor navigation. However,…
This paper proposes a model predictive controller for discrete-time linear systems with additive, possibly unbounded, stochastic disturbances and subject to chance constraints. By computing a polytopic probabilistic positively invariant set…
We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…
Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track…
For linear time-invariant (LTI) systems, the design of an optimal controller is a commonly encountered problem in many applications. Among all the optimization approaches available, the linear quadratic regulator (LQR) methodology certainly…
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…
In this paper, we propose an unifying view of several recently proposed structured sparsity-inducing norms. We consider the situation of a model simultaneously (a) penalized by a set- function de ned on the support of the unknown parameter…