Related papers: Filtering-Linearization: A First-Order Method for …
In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…
We study the safe reinforcement learning problem with nonlinear function approximation, where policy optimization is formulated as a constrained optimization problem with both the objective and the constraint being nonconvex functions. For…
We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective…
In this paper, a tunneling method is developed for nonlinear multiobjective optimization problems using some ideas of the single objective tunneling method. The proposed method does not require any a priori chosen parameters or ordering…
We look at a stochastic time-varying optimization problem and we formulate online algorithms to find and track its optimizers in expectation. The algorithms are derived from the intuition that standard prediction and correction steps can be…
We present a novel methodology for convex optimization algorithm design using ideas from electric RLC circuits. Given an optimization problem, the first stage of the methodology is to design an appropriate electric circuit whose…
In this paper, we address the trajectory planning problem in uncertain nonconvex static and dynamic environments that contain obstacles with probabilistic location, size, and geometry. To address this problem, we provide a risk bounded…
We consider deterministic finite-horizon optimal control problems with a fixed initial state. We introduce an on-line policy iteration method, which, starting from a given policy, however obtained, generates a sequence of cost-improving…
We propose a sampling-based trajectory optimization methodology for constrained problems. We extend recent works on stochastic search to deal with box control constraints,as well as nonlinear state constraints for discrete dynamical…
Motivated by applications in machine learning and operations research, we study regret minimization with stochastic first-order oracle feedback in online constrained, and possibly non-smooth, non-convex problems. In this setting, the…
We introduce a generic scheme for accelerating gradient-based optimization methods in the sense of Nesterov. The approach, called Catalyst, builds upon the inexact accelerated proximal point algorithm for minimizing a convex objective…
Many recent studies on first-order methods (FOMs) focus on \emph{composite non-convex non-smooth} optimization with linear and/or nonlinear function constraints. Upper (or worst-case) complexity bounds have been established for these…
We study the non-smooth optimization problems in machine learning, where both the loss function and the regularizer are non-smooth functions. Previous studies on efficient empirical loss minimization assume either a smooth loss function or…
Momentum-based gradients are essential for optimizing advanced machine learning models, as they not only accelerate convergence but also advance optimizers to escape stationary points. While most state-of-the-art momentum techniques utilize…
In this paper, we propose a framework based on sum-of-squares programming to design iterative first-order optimization algorithms for smooth and strongly convex problems. Our starting point is to develop a polynomial matrix inequality as a…
Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…
This paper addresses the challenge of accommodating nonlinear dynamics and constraints in rapid trajectory optimization, envisioned for use in the context of onboard guidance. We present a novel framework that uniquely employs…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
In this paper, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable…
We introduce a new form of Lagrangian and propose a simple first-order algorithm for nonconvex optimization with nonlinear equality constraints. We show the algorithm generates bounded dual iterates, and establish the convergence to KKT…