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We consider convex optimization problems which are widely used as convex relaxations for low-rank matrix recovery problems. In particular, in several important problems, such as phase retrieval and robust PCA, the underlying assumption in…
In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…
We develop regularization methods to find flat minima while training deep neural networks. These minima generalize better than sharp minima, yielding models outperforming baselines on real-world test data (which may be distributed…
We study the conditions under which one is able to efficiently apply variance-reduction and acceleration schemes on finite sum optimization problems. First, we show that, perhaps surprisingly, the finite sum structure by itself, is not…
We introduce a novel method for solving density-based topology optimization problems: Sigmoidal Mirror descent with a Projected Latent variable (SiMPL). The SiMPL method (pronounced as ``the simple method'') optimizes a design using only…
Motivated by robust matrix recovery problems such as Robust Principal Component Analysis, we consider a general optimization problem of minimizing a smooth and strongly convex loss function applied to the sum of two blocks of variables,…
Splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which the simple pieces of the…
An unsolved issue in widely used methods such as Support Vector Data Description (SVDD) and Small Sphere and Large Margin SVM (SSLM) for anomaly detection is their nonconvexity, which hampers the analysis of optimal solutions in a manner…
Phase retrieval has important applications in optical imaging, communications and sensing. Lifting the dimensionality of the problem allows phase retrieval to be approximated as a convex optimization problem in a higher-dimensional space.…
The paper discusses derivative-free optimization (DFO), which involves minimizing a function without access to gradients or directional derivatives, only function evaluations. Classical DFO methods, which mimic gradient-based methods, such…
For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…
We study a class of non-convex and non-smooth problems with \textit{rank} regularization to promote sparsity in optimal solution. We propose to apply the proximal gradient descent method to solve the problem and accelerate the process with…
In this paper, we consider a class of finite-sum convex optimization problems defined over a distributed multiagent network with $m$ agents connected to a central server. In particular, the objective function consists of the average of $m$…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
Successive quadratic approximations (SQA) are numerically efficient for minimizing the sum of a smooth function and a convex function. The iteration complexity of inexact SQA methods has been analyzed recently. In this paper, we present an…
We consider the gradient (or steepest) descent method with exact line search applied to a strongly convex function with Lipschitz continuous gradient. We establish the exact worst-case rate of convergence of this scheme, and show that this…
In this paper we present a subgradient method with non-monotone line search for the minimization of convex functions with simple convex constraints. Different from the standard subgradient method with prefixed step sizes, the new method…
In a Hilbert setting, we develop a gradient-based dynamic approach for fast solving convex optimization problems. By applying time scaling, averaging, and perturbation techniques to the continuous steepest descent (SD), we obtain…
This paper introduces a new step to the Direct Search Method (DSM) to strengthen its convergence analysis. By design, this so-called covering step may ensure that for all refined points of the sequence of incumbent solutions generated by…
This paper presents an algorithmic framework for the minimization of strictly convex quadratic functions. The framework is flexible and generic. At every iteration the search direction is a linear combination of the negative gradient, as…