Related papers: Continuous-Time Analysis for Minimax and Bilevel P…
We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…
The use of stochastic differential equations in multi-objective optimization has been limited, in practice, by two persistent gaps: incomplete stability analyses and the absence of accessible implementations. We revisit a drift--diffusion…
In this study, we investigate the performance of two novel first-order optimization algorithms, namely the rescaled-gradient flow (RGF) and the signed-gradient flow (SGF). These algorithms are derived from the forward Euler discretization…
In this paper, we develop a scaled gradient-momentum framework for continuous-time optimization that achieves global finite-time convergence. A state-dependent scaling mechanism is introduced to enable classical dynamics, such as…
We propose a novel flexible-step model predictive control algorithm for unknown linear time-invariant discrete-time systems. The goal is to asymptotically stabilize the system without relying on a pre-collected dataset that describes its…
We show that a common Lyapunov matrix exists for the convex combination of two Hurwitz matrices if and only if the intersection of the set of strict Lyapunov matrices for one matrix and the set of non-strict Lyapunov matrices for the other…
The accelerated method in solving optimization problems has always been an absorbing topic. Based on the fixed-time (FxT) stability of nonlinear dynamical systems, we provide a unified approach for designing FxT gradient flows (FxTGFs).…
We study a continuous-time system that solves optimization problems over the set of orthonormal matrices, which is also known as the Stiefel manifold. The resulting optimization flow follows a path that is not always on the manifold but…
Primal-dual algorithms are frequently used for iteratively solving large-scale convex optimization problems. The analysis of such algorithms is usually done on a case-by-case basis, and the resulting guaranteed rates of convergence can be…
We develop an approach for solving one-sided optimal stopping problems in discrete time for general underlying Markov processes on the real line. The main idea is to transform the problem into an auxiliary problem for the ladder height…
We investigate relaxations for a class of discrete bilevel programs where the interaction constraints linking the leader and the follower are linear. Our approach reformulates the upper-level optimality constraints by projecting the…
In this work, we investigate the use of data-driven equation discovery for dynamical systems to model and forecast continuous-time dynamics of unconstrained optimization problems. To avoid expensive evaluations of the objective function and…
We study stability and input-state analysis of three dimensional (3D) incompressible, viscous flows with invariance in one direction. By taking advantage of this invariance property, we propose a class of Lyapunov and storage functionals.…
Distributed optimization has gained significant attention in recent years, primarily fueled by the availability of a large amount of data and privacy-preserving requirements. This paper presents a fixed-time convergent optimization…
In this work, we propose derivative-free framework for bilevel optimization. We consider both the upper and lower-level problems with bound constraints on the variables, as well as general nonlinear constraints, assuming that first-order…
Complex-valued bidirectional associative memory (BAM) neural networks with fractional-order dynamics and delays can exhibit transient instabilities that degrade synchronization and short-horizon predictability. This paper develops a unified…
Bilevel optimization (BO) has recently gained prominence in many machine learning applications due to its ability to capture the nested structure inherent in these problems. Recently, many hypergradient methods have been proposed as…
Stochastic bilevel optimization generalizes the classic stochastic optimization from the minimization of a single objective to the minimization of an objective function that depends the solution of another optimization problem. Recently,…
In this paper, we propose a novel solution for the distributed unconstrained optimization problem where the total cost is the summation of time-varying local cost functions of a group networked agents. The objective is to track the optimal…
We analyze continuous-time models of accelerated gradient methods through deriving conservation laws in dilated coordinate systems. Namely, instead of analyzing the dynamics of $X(t)$, we analyze the dynamics of $W(t)=t^\alpha(X(t)-X_c)$…