Related papers: An extension of hybrid method without extrapolatio…

We study the problem of learning similarity by using nonlinear embedding models (e.g., neural networks) from all possible pairs. This problem is well-known for its difficulty of training with the extreme number of pairs. For the special…

In this paper, we develop a new type of accelerated algorithms to solve some classes of maximally monotone equations as well as monotone inclusions. Instead of using Nesterov's accelerating approach, our methods rely on a so-called…

This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…

This paper presents a novel hybrid approach that integrates linear programming (LP) within the loss function of an unsupervised machine learning model. By leveraging the strengths of both optimization techniques and machine learning, this…

Gradient methods have applications in multiple fields, including signal processing, image processing, and dynamic systems. In this paper, we present a nonlinear gradient method for solving convex supra-quadratic functions by developing the…

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…

In this paper, we propose a novel extrapolation coefficient scheme within a new extrapolation term and develop an accelerated proximal gradient algorithm. We establish that the algorithm achieves a sublinear convergence rate. The proposed…

In this paper, we propose a conditional gradient method for solving constrained vector optimization problems with respect to a partial order induced by a closed, convex and pointed cone with nonempty interior. When the partial order under…

In this work, we propose an outer approximation algorithm for solving bounded convex vector optimization problems (CVOPs). The scalarization model solved iteratively within the algorithm is a modification of the norm-minimizing…

Processing sets or other unordered, potentially variable-sized inputs in neural networks is usually handled by aggregating a number of input tensors into a single representation. While a number of aggregation methods already exist from…

Large-scale unconstrained optimization is a fundamental and important class of, yet not well-solved problems in numerical optimization. The main challenge in designing an algorithm is to require a few storage locations or very inexpensive…

In this paper, we consider the equilibrium problems and also their regularized problems under the setting of Hadamard spaces. The solution to the regularized problem is represented in terms of resolvent operators. As an essential machinery…

We present a novel method for approximately equilibrating a matrix $A \in {\bf R}^{m \times n}$ using only multiplication by $A$ and $A^T$. Our method is based on convex optimization and projected stochastic gradient descent, using an…

Bilevel optimization is an important class of optimization problems where one optimization problem is nested within another. While various methods have emerged to address unconstrained general bilevel optimization problems, there has been a…

The data-compatibility approach to constrained optimization, proposed here, strives to a point that is "close enough" to the solution set and whose target function value is "close enough" to the constrained minimum value. These notions can…

A recently introduced general-purpose heuristic for finding high-quality solutions for many hard optimization problems is reviewed. The method is inspired by recent progress in understanding far-from-equilibrium phenomena in terms of {\em…

We consider in this paper a class of composite optimization problems whose objective function is given by the summation of a general smooth and nonsmooth component, together with a relatively simple nonsmooth term. We present a new class of…

Hybrid optimization algorithms have gained popularity as it has become apparent there cannot be a universal optimization strategy which is globally more beneficial than any other. Despite their popularity, hybridization frameworks require…

Recently, minimax optimization received renewed focus due to modern applications in machine learning, robust optimization, and reinforcement learning. The scale of these applications naturally leads to the use of first-order methods.…