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This work examines the conditions for asymptotic and exponential convergence of saddle flow dynamics of convex-concave functions. First, we propose an observability-based certificate for asymptotic convergence, directly bridging the gap…
This paper studies equality-constrained minimization problems through the lens of feedback control. We introduce a unified control-theoretic framework by showing that a PID feedback law acting on the dual variable induces the PID…
In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…
We propose a modified primal-dual method for general convex optimization problems with changing constraints. We obtain properties of Lagrangian saddle points for these problems which enable us to establish convergence of the proposed…
This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…
We examine stability properties of primal-dual gradient flow dynamics for composite convex optimization problems with multiple, possibly nonsmooth, terms in the objective function under the generalized consensus constraint. The proposed…
This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…
A transformed primal-dual (TPD) flow is developed for a class of nonlinear smooth saddle point system. The flow for the dual variable contains a Schur complement which is strongly convex. Exponential stability of the saddle point is…
Continuous time primal-dual gradient dynamics that find a saddle point of a Lagrangian of an optimization problem have been widely used in systems and control. While the global asymptotic stability of such dynamics has been well-studied, it…
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 studies the projected saddle-point dynamics associated to a convex-concave function, which we term saddle function. The dynamics consists of gradient descent of the saddle function in variables corresponding to convexity and…
Primal-dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal-dual gradient dynamics (Aug-PDGD)…
We present a parallelized primal-dual algorithm for solving constrained convex optimization problems. The algorithm is "block-based," in that vectors of primal and dual variables are partitioned into blocks, each of which is updated only by…
We present a parallelized primal-dual algorithm for solving constrained convex optimization problems. The algorithm is "block-based," in that vectors of primal and dual variables are partitioned into blocks, each of which is updated only by…
In this paper, we study saddle point (SP) problems, focusing on convex-concave optimization involving functions that satisfy either two-sided quadratic functional growth (QFG) or two-sided quadratic gradient growth (QGG)--novel conditions…
This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems…
We introduce a novel primal-dual flow for affine constrained convex optimization problems. As a modification of the standard saddle-point system, our primal-dual flow is proved to possess the exponential decay property, in terms of a…
A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…
We develop a second order primal-dual method for optimization problems in which the objective function is given by the sum of a strongly convex twice differentiable term and a possibly nondifferentiable convex regularizer. After introducing…
Non-convex functional constrained optimization problems have gained substantial attention in machine learning and data science, addressing broad requirements that typically go beyond the often performance-centric objectives. An influential…