Related papers: Generalized Left-Localized Cayley Parametrization …

This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…

Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…

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…

Distributed stochastic optimization has drawn great attention recently due to its effectiveness in solving large-scale machine learning problems. Though numerous algorithms have been proposed and successfully applied to general practical…

We propose a localized approach to multiple kernel learning that can be formulated as a convex optimization problem over a given cluster structure. For which we obtain generalization error guarantees and derive an optimization algorithm…

There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…

Symmetric positive definite (SPD) matrices used as feature descriptors in image recognition are usually high dimensional. Traditional manifold learning is only applicable for reducing the dimension of high-dimensional vector-form data. For…

In this paper, we study a class of stochastic bilevel optimization problems, also known as stochastic simple bilevel optimization, where we minimize a smooth stochastic objective function over the optimal solution set of another stochastic…

Optimization techniques are at the core of many scientific and engineering disciplines. The steepest descent methods play a foundational role in this area. In this paper we studied a generalized steepest descent method on Riemannian…

Recently, the proximal Newton-type method and its variants have been generalized to solve composite optimization problems over the Stiefel manifold whose objective function is the summation of a smooth function and a nonsmooth function. In…

We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…

Distributed optimization is an important direction of research in modern optimization theory. Its applications include large scale machine learning, distributed signal processing and many others. The paper studies decentralized min-max…

Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…

$\renewcommand{\Re}{\mathbb{R}}$ We develop a general randomized technique for solving "implic it" linear programming problems, where the collection of constraints are defined implicitly by an underlying ground set of elements. In many…

Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to…

This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…

This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…

Designing a fast and efficient optimization method with local optima avoidance capability on a variety of optimization problems is still an open problem for many researchers. In this work, the concept of a new global optimization method…

We propose a modified primal-dual method for general convex optimization problems with changing constraints. We obtain properties of Lagrangian saddle points for these problems which enable us to establish convergence of the proposed…

Principal component analysis is a simple yet useful dimensionality reduction technique in modern machine learning pipelines. In consequential domains such as college admission, healthcare and credit approval, it is imperative to take into…