Related papers: Global Convergence of Control-Based Lagrangian Flo…
Motivated by an inertial primal-dual dynamical system with vanishing damping, we propose a class of accelerated augmented Lagrangian methods with Nesterov extrapolation parameters for a linearly constrained convex optimization problem with…
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 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 $O(1/K^2)$…
We study non-convex subgradient flows for training two-layer ReLU neural networks from a convex geometry and duality perspective. We characterize the implicit bias of unregularized non-convex gradient flow as convex regularization of an…
We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of…
This article presents a unified synchronization framework with application to precision formation flying spacecraft. Central to the proposed innovation, in applying synchronization to both translational and rotational dynamics in the…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
The mirror descent algorithm is known to be effective in situations where it is beneficial to adapt the mirror map to the underlying geometry of the optimization model. However, the effect of mirror maps on the geometry of distributed…
We consider a general multi-agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint, a global equality constraint, and a global constraint set.…
This paper develops a robust fixed time optimization framework for constrained problems that guarantees exact constraint satisfaction and convergence to KKT points within fixed time , independent of initial conditions. The approach treats…
Distributed optimization algorithms are used in a wide variety of problems involving complex network systems where the goal is for a set of agents in the network to solve a network-wide optimization problem via distributed update rules. In…
In this paper we propose a primal-dual dynamical approach to the minimization of a structured convex function consisting of a smooth term, a nonsmooth term, and the composition of another nonsmooth term with a linear continuous operator. In…
This paper develops a sliding mode control based frame work for equality constrained optimization by reformulation the first order Karush Kuhn Tucker conditions as control affine dynamical system. The optimization variables are treated as…
Distributed control problems under some specific information constraints can be formulated as (possibly infinite dimensional) convex optimization problems. The underlying motivation of this work is to develop an understanding of the optimal…
Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…
Large-scale constrained optimization is pivotal in modern scientific, engineering, and industrial computation, often involving complex systems with numerous variables and constraints. This paper provides a unified and comprehensive…
We develop an efficient method for solving non-convex constrained optimization problems that are pervasive in economics. The optimal solution to these problems often involves randomization. We employ a Lagrangian framework and prove that…
The paper is about the data-driven computation of optimal control for a class of control affine deterministic nonlinear systems. We assume that the control dynamical system model is not available, and the only information about the system…
This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal…
In this paper, we aim at unifying, simplifying and improving the convergence rate analysis of Lagrangian-based methods for convex optimization problems. We first introduce the notion of nice primal algorithmic map, which plays a central…