Related papers: Dynamic FISTA for Convex Composite Bi-Level Optimi…
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…
We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…
Many large-scale constrained optimization problems can be formulated as bilevel distributed optimization tasks over undirected networks, where agents collaborate to minimize a global cost function while adhering to constraints, relying only…
In this paper, we develop an interior-point method for solving a class of convex optimization problems with time-varying objective and constraint functions. Using log-barrier penalty functions, we propose a continuous-time dynamical system…
We analyze the convergence rate of an accelerated backward forward method for solving convex composite optimization problems. The method was developed by Taylor, Hendrickx and Glineur, and is different from the FISTA algorithm in its…
In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…
By adjusting both the structural shape and fiber orientation, this research aims to optimize the design of Fiber Reinforced Composite structures. The structural geometry is represented by a level set function, which is approximated by…
Bilevel optimization is a hierarchical framework where an upper-level optimization problem is constrained by a lower-level problem, commonly used in machine learning applications such as hyperparameter optimization. Existing bilevel…
Bilevel optimization is widely applied in many machine learning tasks such as hyper-parameter learning, meta learning and reinforcement learning. Although many algorithms recently have been developed to solve the bilevel optimization…
Optimization problems emerging in most of the real-world applications are dynamic, where either the objective function or the constraints change continuously over time. This paper proposes projected primal-dual dynamical system approaches…
For first-order smooth optimization, the research on the acceleration phenomenon has a long-time history. Until recently, the mechanism leading to acceleration was not successfully uncovered by the gradient correction term and its…
An usual problem in statistics consists in estimating the minimizer of a convex function. When we have to deal with large samples taking values in high dimensional spaces, stochastic gradient algorithms and their averaged versions are…
We consider a generic min-max multi-objective bilevel optimization problem with applications in robust machine learning such as representation learning and hyperparameter optimization. We design MORBiT, a novel single-loop gradient…
In recent years, a variety of gradient-based methods have been developed to solve Bi-Level Optimization (BLO) problems in machine learning and computer vision areas. However, the theoretical correctness and practical effectiveness of these…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
This paper studies second-order methods for nonconvex-strongly-convex bilevel optimization. We propose a novel fully second-order bilevel approximation method (FSBA) that achieves an iteration complexity of…
We present a distributed proximal-gradient method for optimizing the average of convex functions, each of which is the private local objective of an agent in a network with time-varying topology. The local objectives have distinct…
A subgradient method is presented for solving general convex optimization problems, the main requirement being that a strictly-feasible point is known. A feasible sequence of iterates is generated, which converges to within user-specified…
In this paper, a convex optimization-based method is proposed for numerically solving dynamic programs in continuous state and action spaces. The key idea is to approximate the output of the Bellman operator at a particular state by the…
This paper investigates the convex optimization problem with general convex inequality constraints. To cope with this problem, a discrete-time algorithm, called augmented primal-dual gradient algorithm (Aug-PDG), is studied and analyzed. It…