相关论文: Limit Behavior and the Role of Augmentation in Pro…

We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…

Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…

We propose an algorithm using method of evolving junctions to solve the optimal path planning problems with piece-wise constant flow fields. In such flow fields with a convex Lagrangian in the objective function, we can prove that the…

In this paper, we present a novel control scheme for feedback optimization. That is, we propose a discrete-time controller that can steer the steady state of a physical plant to the solution of a constrained optimization problem without…

Motion planning for manipulators under task space constraints is difficult as it constrains the joint configurations to always lie on an implicitly defined manifold. It is possible to view task constrained motion planning as an optimization…

In this work we study the convergence of gradient methods for nonconvex optimization problems -- specifically the effect of the problem formulation to the convergence behavior of the solution of a gradient flow. We show through a simple…

We examine online safe multi-agent reinforcement learning using constrained Markov games in which agents compete by maximizing their expected total rewards under a constraint on expected total utilities. Our focus is confined to an episodic…

We propose a primal-dual smoothing framework for finding a near-stationary point of a class of non-smooth non-convex optimization problems with max-structure. We analyze the primal and dual gradient complexities of the framework via two…

Model instability and poor prediction of long-term behavior are common problems when modeling dynamical systems using nonlinear "black-box" techniques. Direct optimization of the long-term predictions, often called simulation error…

We propose an inexact proximal augmented Lagrangian method (P-ALM) for nonconvex structured optimization problems. The proposed method features an easily implementable rule not only for updating the penalty parameters, but also for…

We study the convergence rates of the classical Lagrangian-based methods and their variants for solving convex optimization problems with equality constraints. We present a generalized prediction-correction framework to establish $O(1/K^2)$…

Nonconvex optimization underlies many modern machine learning and control tasks, where saddle points pose the dominant obstacle to reliable convergence in high-dimensional settings. Escaping these saddle points deterministically using…

In this paper, we study the gradient descent-ascent method for convex-concave saddle-point problems. We derive a new non-asymptotic global convergence rate in terms of distance to the solution set by using the semidefinite programming…

In this paper, we employ the concept of quasi-relative interior to analyze the method of Lagrange multipliers and establish strong Lagrangian duality for nonsmooth convex optimization problems in Hilbert spaces. Then, we generalize the…

Motivated by a constrained minimization problem, it is studied the gradient flows with respect to Hessian Riemannian metrics induced by convex functions of Legendre type. The first result characterizes Hessian Riemannian structures on…

This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…

Generalized nonlinear programming is considered without any convexity assumption, capturing a variety of problems that include nonsmooth objectives, combinatorial structures, and set-membership nonlinear constraints. We extend the augmented…

We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function…

Under appropriate cooperation protocols and parameter choices, fully decentralized solutions for stochastic optimization have been shown to match the performance of centralized solutions and result in linear speedup (in the number of…

The optimal allocation of resources for maximizing influence, spread of information or coverage, has gained attention in the past years, in particular in machine learning and data mining. But in applications, the parameters of the problem…