Related papers: Newton-type method for bilevel programs with linea…
This work is concerned with the efficient optimization method for solving a large class of optimal mass transport problems. An inexact primal-dual algorithm is presented from the time discretization of a proper dynamical system, and by…
The ability to efficiently solve topology optimization problems is of great importance for many practical applications. Hence, there is a demand for efficient solution algorithms. In this paper, we propose novel quasi-Newton methods for…
In many applications, including Stackelberg games, machine learning, and power systems \cite{Mackay2018Selftuning,Heinrich1952The,Wang2021Bi-Level}, the decisions in a minimax optimization problem can be constrained by a solution to an…
Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…
We propose two variants of Newton method for solving unconstrained minimization problem. Our method leverages optimization techniques such as penalty and augmented Lagrangian method to generate novel variants of the Newton method namely the…
Support vector classification (SVC) with logistic loss has excellent theoretical properties in classification problems where the label values are not continuous. In this paper, we reformulate the hyperparameter selection for SVC with…
In this paper we study a class of unconstrained and constrained bilevel optimization problems in which the lower level is a possibly nonsmooth convex optimization problem, while the upper level is a possibly nonconvex optimization problem.…
Bilevel programs are optimization problems where some variables are solutions to optimization problems themselves, and they arise in a variety of control applications, including: control of vehicle traffic networks, inverse reinforcement…
This paper studies bilevel polynomial optimization problems. To solve them, we give a method based on polynomial optimization relaxations. Each relaxation is obtained from the Kurash-Kuhn-Tucker (KKT) conditions for the lower level…
We present a novel Newton-type method for distributed optimization, which is particularly well suited for stochastic optimization and learning problems. For quadratic objectives, the method enjoys a linear rate of convergence which provably…
We consider the entropic regularization of discretized optimal transport and propose to solve its optimality conditions via a logarithmic Newton iteration. We show a quadratic convergence rate and validate numerically that the method…
We study the problem of minimizing a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of…
This paper addresses the problem of Unbalanced Optimal Transport (UOT) in which the marginal conditions are relaxed (using weighted penalties in lieu of equality) and no additional regularization is enforced on the OT plan. In this context,…
We study a semismooth Newton-type method for the nearest doubly stochastic matrix problem where both differentiability and nonsingularity of the Jacobian can fail. The optimality conditions for this problem are formulated as a system of…
Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…
Newton's method may exhibit slower convergence than vanilla Gradient Descent in its initial phase on strongly convex problems. Classical Newton-type multilevel methods mitigate this but, like Gradient Descent, achieve only linear…
Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
In this paper, a globally convergent Newton-type proximal gradient method is developed for composite multi-objective optimization problems where each objective function can be represented as the sum of a smooth function and a nonsmooth…
One of the most important problems in the field of distributed optimization is the problem of minimizing a sum of local convex objective functions over a networked system. Most of the existing work in this area focus on developing…
This paper considers the simple bilevel optimization (SBO) problem, which minimizes a composite convex function over the optimal solution set of another composite convex minimization problem. We first show that this bilevel problem is…