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We propose a new modified primal-dual proximal best approximation method for solving convex not necessarily differentiable optimization problems. The novelty of the method relies on introducing memory by taking into account iterates…
In this paper we propose a unified two-phase scheme for convex optimization to accelerate: (1) the adaptive cubic regularization methods with exact/inexact Hessian matrices, and (2) the adaptive gradient method, without any knowledge of the…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…
We present a method for finding lower bounds on the global infima of integral variational problems, wherein $\int_\Omega f(x,u(x),\nabla u(x)){\rm d}x$ is minimized over functions $u\colon\Omega\subset\mathbb{R}^n\to\mathbb{R}^m$ satisfying…
In this paper, we consider the problem of minimizing a difference-of-convex objective over a nonlinear conic constraint, where the cone is closed, convex, pointed and has a nonempty interior. We assume that the support function of a compact…
In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the…
Inspired by recent work on safe feature elimination for $1$-norm regularized least-squares, we develop strategies to eliminate features from convex optimization problems with non-negativity constraints. Our strategy is safe in the sense…
Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
We present a new approach for computing approximate global minimizers to a large class of non-local pairwise interaction problems defined over probability distributions. The approach predicts candidate global minimizers, with a recovery…
Convex regression (CR) is an approach for fitting a convex function to a finite number of observations. It arises in various applications from diverse fields such as statistics, operations research, economics, and electrical engineering.…
We propose a numerical method to solve the Monge-Ampere equation which admits a classical convex solution. The Monge-Ampere equation is reformulated into an equivalent first-order system. We adopt a novel reconstructed discontinuous…
Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by…
Sparse approximate solutions to linear equations are classically obtained via L1 norm regularized least squares, but this method often underestimates the true solution. As an alternative to the L1 norm, this paper proposes a class of…
In this paper we derive a moment relaxation for large-scale nonsmooth optimization problems with graphical structure and spherical constraints. In contrast to classical moment relaxations for global polynomial optimization that suffer from…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
Rank minimization (RM) is a wildly investigated task of finding solutions by exploiting low-rank structure of parameter matrices. Recently, solving RM problem by leveraging non-convex relaxations has received significant attention. It has…
In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…