Related papers: A Hybrid Algorithm for Convex Semidefinite Optimiz…
Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a…
We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…
We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous…
We develop new adaptive algorithms for variational inequalities with monotone operators, which capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Our algorithms automatically adapt to…
Various optimal gradient-based algorithms have been developed for smooth nonconvex optimization. However, many nonconvex machine learning problems do not belong to the class of smooth functions and therefore the existing algorithms are…
Many problems of theoretical and practical interest involve finding a convex or concave function. For instance, optimization problems such as finding the projection on the convex functions in $H^k(\Omega)$, or some problems in economics. In…
We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
We investigate the techniques and ideas used in the convergence analysis of two proximal ADMM algorithms for solving convex optimization problems involving compositions with linear operators. Besides this, we formulate a variant of the ADMM…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
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…
In the paper, we develop a composite version of Mirror Prox algorithm for solving convex-concave saddle point problems and monotone variational inequalities of special structure, allowing to cover saddle point/variational analogies of what…
We consider the task of decentralized minimization of the sum of smooth strongly convex functions stored across the nodes of a network. For this problem, lower bounds on the number of gradient computations and the number of communication…
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper-C2 objective functions is proposed and analyzed. Upper-C2 is a weakly concave property that exists in difference of convex (DC) functions and…
Federated learning enables training on a massive number of edge devices. To improve flexibility and scalability, we propose a new asynchronous federated optimization algorithm. We prove that the proposed approach has near-linear convergence…
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…
We develop \emph{geometric optimisation} on the manifold of Hermitian positive definite (HPD) matrices. In particular, we consider optimising two types of cost functions: (i) geodesically convex (g-convex); and (ii) log-nonexpansive (LN).…
This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…
We propose a method for low-rank semidefinite programming in application to the semidefinite relaxation of unconstrained binary quadratic problems. The method improves an existing solution of the semidefinite programming relaxation to…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.