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This paper presents a Successive Convexification ($ \texttt{SCvx} $) algorithm to solve a class of non-convex optimal control problems with certain types of state constraints. Sources of non-convexity may include nonlinear dynamics and…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
We propose a convex optimization procedure for black-box identification of nonlinear state-space models for systems that exhibit stable limit cycles (unforced periodic solutions). It extends the "robust identification error" framework in…
In this paper, we propose a very efficient numerical method based on the L-BFGS-B algorithm for identifying linear and nonlinear discrete-time state-space models, possibly under $\ell_1$ and group-Lasso regularization for reducing model…
We present FilterDDP, a differential dynamic programming algorithm for solving discrete-time, optimal control problems (OCPs) with nonlinear equality constraints. Unlike prior methods based on merit functions or the augmented Lagrangian…
The Sequential Linear Quadratic (SLQ) algorithm is a continuous-time variant of the well-known Differential Dynamic Programming (DDP) technique with a Gauss-Newton Hessian approximation. This family of methods has gained popularity in the…
The combination of machine learning (ML) and sparsity-promoting techniques is enabling direct extraction of governing equations from data, revolutionizing computational modeling in diverse fields of science and engineering. The discovered…
We propose a technique for the design and analysis of adaptation algorithms in dynamical systems. The technique applies both to systems with conventional Lyapunov-stable target dynamics and to ones of which the desired dynamics around the…
We study how to solve semidefinite programming relaxations for large scale polynomial optimization. When interior-point methods are used, typically only small or moderately large problems could be solved. This paper studies regularization…
Modeling realistic fluid and plasma flows is computationally intensive, motivating the use of reduced-order models for a variety of scientific and engineering tasks. However, it is challenging to characterize, much less guarantee, the…
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
In this paper, we establish the local superlinear convergence property of some polynomial-time interior-point methods for an important family of conic optimization problems. The main structural property used in our analysis is the…
The linear programming (LP) approach has a long history in the theory of approximate dynamic programming. When it comes to computation, however, the LP approach often suffers from poor scalability. In this work, we introduce a relaxed…
Stochastic gradient descent with momentum (SGDM) is the dominant algorithm in many optimization scenarios, including convex optimization instances and non-convex neural network training. Yet, in the stochastic setting, momentum interferes…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…
Large-scale non-convex sparsity-constrained problems have recently gained extensive attention. Most existing deterministic optimization methods (e.g., GraSP) are not suitable for large-scale and high-dimensional problems, and thus…
We provide an algorithm for the simultaneous system identification and model predictive control of nonlinear systems. The algorithm has finite-time near-optimality guarantees and asymptotically converges to the optimal (non-causal)…
Today's complex robotic designs comprise in some cases a large number of degrees of freedom, enabling for multi-objective task resolution (e.g., humanoid robots or aerial manipulators). This paper tackles the stability problem of a…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…