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Convergence analysis of accelerated first-order methods for convex optimization problems are presented from the point of view of ordinary differential equation solvers. A new dynamical system, called Nesterov accelerated gradient flow, has…
Chandrasekaran, Parrilo and Willsky (2010) proposed a convex optimization problem to characterize graphical model selection in the presence of unobserved variables. This convex optimization problem aims to estimate an inverse covariance…
This report describes the experimental analysis of proposed underwater image enhancement algorithms based on partial differential equations (PDEs). The algorithms perform simultaneous smoothing and enhancement due to the combination of both…
We propose two new alternating direction methods to solve "fully" nonsmooth constrained convex problems. Our algorithms have the best known worst-case iteration-complexity guarantee under mild assumptions for both the objective residual and…
A global optimization framework, acronymed COMBEO (Change OfMeasure Based Evolutionary Optimization), is proposed. An important aspect in the development is a set of derivative-free additive directional terms obtainable through a change of…
A fast method for dynamic aperture (DA) optimization of storage rings has been developed through the use of reversal integration. While chaotic dynamical systems have exact time-reversal symmetry, numerical forward integration differs from…
In this paper, we propose a novel approach for underwater image color correction based on a Tikhonov type optimization model in the CIELAB color space. It presents a new variational interpretation of the complementary adaptation theory in…
Asynchronous algorithms have attracted much attention recently due to the crucial demands on solving large-scale optimization problems. However, the accelerated versions of asynchronous algorithms are rarely studied. In this paper, we…
Recently, the joint design of optical systems and downstream algorithms is showing significant potential. However, existing rays-described methods are limited to optimizing geometric degradation, making it difficult to fully represent the…
We implement the adaptive step size scheme from the optimization methods AdaGrad and Adam in a novel variant of the Proximal Gradient Method (PGM). Our algorithm, dubbed AdaProx, avoids the need for explicit computation of the Lipschitz…
This report describes the experimental results obtained using a proposed variational Retinex algorithm for controlled illumination correction. Two colour restoration and enhancement schemes of the algorithm are presented for drastically…
We propose a dynamic spectrum access scheme where secondary users recommend "good" channels to each other and access accordingly. We formulate the problem as an average reward based Markov decision process. We show the existence of the…
We analyze fast diagonal methods for simple bilevel programs. Guided by the analysis of the corresponding continuous-time dynamics, we provide a unified convergence analysis under general geometric conditions, including H\"olderian growth…
This paper presents a new method, called FlexiCurve, for photo enhancement. Unlike most existing methods that perform image-to-image mapping, which requires expensive pixel-wise reconstruction, FlexiCurve takes an input image and estimates…
This work proposes an accelerated primal-dual dynamical system for affine constrained convex optimization and presents a class of primal-dual methods with nonergodic convergence rates. In continuous level, exponential decay of a novel…
In this paper, we propose a second-order continuous primal-dual dynamical system with time-dependent positive damping terms for a separable convex optimization problem with linear equality constraints. By the Lyapunov function approach, we…
Although data augmentation is a powerful technique for improving the performance of image classification tasks, it is difficult to identify the best augmentation policy. The optimal augmentation policy, which is the latent variable, cannot…
For large model spaces, the potential entrapment of Markov chain Monte Carlo (MCMC) based methods with spike-and-slab priors poses significant challenges in posterior computation in regression models. On the other hand, maximum a posteriori…
Recently there were proposed some innovative convex optimization concepts, namely, relative smoothness [1] and relative strong convexity [2,3]. These approaches have significantly expanded the class of applicability of gradient-type methods…
Bilevel optimization is a field of significant theoretical and practical interest, yet solving such optimization problems remains challenging. Evolutionary methods have been employed to address these problems in the black-box setting;…