arXiv subjects

Kok Lay Teo

Publications and source records attributed to Kok Lay Teo.

5 recordsLinked to original sources

arXiv2026

Inertial Primal-Dual Dynamics Methods Featuring Implicit Hessian-Driven Damping for Convex Optimization Problems in Continuous and Discrete Time

This paper investigates inertial primal-dual dynamics with implicit Hessian-driven damping for strongly convex optimization problems with linear equality constraints. We first establish fast convergence rates for the objective function value error, the feasibility measure, and both the trajectory and its corresponding velocity vector. By appropriately adjusting parameters, we show that the proposed system achieves exponential convergence rates. Through implicit time discretization of the dynamical system, we derive an inertial accelerated primal-dual algorithm for solving the strongly convex optimization problems. Using Lyapunov-based method, we show that the proposed algorithm achieves convergence rates consistent with those of its continuous-time counterpart. We also extend the obtained results to non-smooth convex optimization case. Furthermore, we conduct numerical experiments to illustrate theoretical results.

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arXiv2026

Primal-dual dynamical systems with closed-loop control for convex optimization in continuous and discrete time

This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal" + ``first-order dual'' continuous-time dynamical system, in which both the time scaling and Hessian-driven damping are governed by a feedback control of the gradient for the Lagrangian function. This system achieves the fast convergence rates for the primal-dual gap, the feasibility violation, and the objective residual along its trajectory. Subsequently, by time discretization of this system, we develop an accelerated primal-dual algorithm with a gradient-defined adaptive step size. We also obtain convergence rates for the primal-dual gap, the feasibility violation, and the objective residual. Furthermore, we provide numerical results to demonstrate the practical efficacy and superior performance of the proposed algorithm.

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arXiv2025

Inertial accelerated primal-dual algorithms for non-smooth convex optimization problems with linear equality constraints

This paper is devoted to the study of an inertial accelerated primal-dual algorithm, which is based on a second-order differential system with time scaling, for solving a non-smooth convex optimization problem with linear equality constraints. We first introduce a second-order differential system with time scaling associated with the non-smooth convex optimization problem, and then obtain fast convergence rates for the primal-dual gap, the feasibility violation, and the objective residual along the trajectory generated by this system. Subsequently, based on the setting of the parameters involved, we propose an inertial accelerated primal-dual algorithm from the time discretization of this system. We also establish fast convergence rates for the primal-dual gap, the feasibility violation, and the objective residual. Furthermore, we demonstrate the efficacy of the proposed algorithm through numerical experiments.

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arXiv2024

Tikhonov regularization of second-order plus first-order primal-dual dynamical systems for separable convex optimization

This paper deals with a Tikhonov regularized second-order plus first-order primal-dual dynamical system with time scaling for separable convex optimization problems with linear equality constraints. This system consists of two second-order ordinary differential equations for the primal variables and one first-order ordinary differential equation for the dual variable.By utilizing the Lyapunov analysis approach, we obtain the convergence properties of the primal-dual gap, the objective function error, the feasibility measure and the gradient norm of the objective function along the trajectory. We also establish the strong convergence of the primal trajectory generated by the dynamical system towards the minimal norm solution of the separable convex optimization problem. Furthermore, we give numerical experiments to illustrate the theoretical results, showing that our dynamical system performs better than those in the literature in terms of convergence rates.

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arXiv2016

A robust optimal control problem with moment constraints on distribution: theoretical analysis and an algorithm

We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as the worst-case expectation over a set of possible distributions of the uncertain parameter. This ambiguity set of distributions is, in turn, defined by the first two moments of the random variables involved. The optimal control is found by minimizing the worst-case expectation over all possible distributions in this set. If the distributions are discrete, the stochastic min-max optimal control problem can be converted into a convensional optimal control problem via duality, which is then approximated as a finite-dimensional optimization problem via the control parametrization. We derive necessary conditions of optimality and propose an algorithm to solve the approximation optimization problem. The results of discrete probability distribution are then extended to the case with one dimensional continuous stochastic variable by applying the control parametrization methodology on the continuous stochastic variable, and the convergence results are derived. A numerical example is present to illustrate the potential application of the proposed model and the effectiveness of the algorithm.

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