Related papers: Harnessing structure in composite nonsmooth minimi…
While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…
We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…
Proximal operators with affine constraints arise in numerous models in nonconvex projection, composite optimization, and structured regularization. However, their efficient computation remains challenging due to the simultaneous presence of…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…
This work concerns the local convergence theory of Newton and quasi-Newton methods for convex-composite optimization: minimize f(x):=h(c(x)), where h is an infinite-valued proper convex function and c is C^2-smooth. We focus on the case…
An algorithm framework is proposed for minimizing nonsmooth functions. The framework is variable-metric in that, in each iteration, a step is computed using a symmetric positive definite matrix whose value is updated as in a quasi-Newton…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
Within the unmanageably large class of nonconvex optimization, we consider the rich subclass of nonsmooth problems that have composite objectives---this already includes the extensively studied convex, composite objective problems as a…
Many machine learning techniques sacrifice convenient computational structures to gain estimation robustness and modeling flexibility. However, by exploring the modeling structures, we find these "sacrifices" do not always require more…
This paper concerns the minimization of the composition of a nonsmooth convex function and a $\mathcal{C}^{1,1}$ mapping $F$ over a $\mathcal{C}^2$-smooth embedded closed submanifold $\mathcal{M}$. For this class of nonconvex and nonsmooth…
We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle…
Based on the ideas of arXiv:1710.06612, we consider the problem of minimization of the Holder-continuous non-smooth functional $f$ with non-positive convex (generally, non-smooth) Lipschitz-continuous functional constraint. We propose some…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
This work aims to solve a stochastic nonconvex nonsmooth composite optimization problem. Previous works on composite optimization problem requires the major part to satisfy Lipschitz smoothness or some relaxed smoothness conditions, which…
The proximal gradient algorithm for minimizing the sum of a smooth and a nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may…
We introduce a conceptually simple and efficient algorithm for seamless parametrization, a key element in constructing quad layouts and texture charts on surfaces. More specifically, we consider the construction of parametrizations with…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
We study minimization of a structured objective function, being the sum of a smooth function and a composition of a weakly convex function with a linear operator. Applications include image reconstruction problems with regularizers that…
We consider trust-region methods for solving optimization problems where the objective is the sum of a smooth, nonconvex function and a nonsmooth, convex regularizer. We extend the global convergence theory of such methods to include…