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Robust Design of Slow-Light Tapers in Periodic Waveguides
robust optimization PDE-constrained optimization shape optimization coupling taper
2015/7/9
This paper concerns the design of tapers for coupling power between uniform and slow-light periodic waveguides. New optimization methods are described for designing robust tapers, which not only perfo...
l_1 Trend Filtering
detrending regularization Hodrick–Prescott fi ltering piecewise linear fi tting
2015/7/9
The problem of estimating underlying trends in time series data arises in a variety of disciplines. In this paper we propose a variation on Hodrick-Prescott (H-P) filtering, a widely used method for t...
Subspaces that Minimize the Condition Number of a Matrix
Subspaces Minimize Condition Number Matrix
2015/7/9
We define the condition number of a nonsingular matrix on a subspace, and consider the problem of finding a subspace of given dimension that minimizes the condition number of a given matrix. We give a...
Estimation of Faults in DC Electrical Power System
Estimation Faults DC Electrical Power System
2015/7/9
This paper demonstrates a novel optimization-based approach to estimating fault states in a DC power system. The model includes faults changing the circuit topology along with sensor faults. Our appro...
Mixed Linear System Estimation and Identification
Statistical estimation Convex relaxation Interior-point methods
2015/7/9
We consider a mixed linear system model, with both continuous and discrete inputs and outputs, described by a coefficient matrix and a set of noise variances. When the discrete inputs and outputs are ...
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
Distributed Optimization Statistical Learning via Alternating Direction Method Multipliers
2015/7/9
Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasi...
This paper considers the problem of fitting regression models to historical fleet data with mixed effects, which arises in the context of statistical monitoring of data from a fleet (population) of si...
In this paper, we describe the embedded conic solver (ECOS), an interior-point solver for second-order cone programming (SOCP) designed specifically for embedded applications. ECOS is written in low f...
Proximal Algorithms
Proximal Algorithms
2015/7/9
This monograph is about a class of optimization algorithms called proximal algorithms. Much like Newton's method is a standard tool for solving unconstrained smooth optimization problems of modest siz...
Quadratic Approximate Dynamic Programming for Input-Affine Systems
approximate dynamic programming stochastic control convex optimization
2015/7/9
We consider the use of quadratic approximate value functions for stochastic control problems with input-affine dynamics and convex stage cost and constraints. Evaluating the approximate dynamic progra...
Variations and Extensions of the Convex-Concave Procedure
Variations Extensions Convex-Concave Procedure
2015/7/9
We investigate the convex-concave procedure (CCP), a local heuristic that utilizes the tools of convex optimization to find local optima of difference of convex (DC) programming problems. The class of...
Metric Selection in Fast Dual Forward Backward Splitting
Metric Selection Fast Dual Forward Backward Splitting
2015/7/9
The performance of fast forward-backward splitting, or equivalently fast proximal gradient methods, is susceptible to conditioning of the optimization problem data. This conditioning is related to a m...
First order optimization methods often perform poorly on ill-conditioned optimization problems. However, by preconditioning the problem data and solving the preconditioned problem, the performance of ...
Diagonal Scaling in Douglas-Rachford Splitting and ADMM
Diagonal Scaling Douglas-Rachford Splitting ADMM
2015/7/9
Recently, several convergence rate results for Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) have been presented in the literature. In this paper, we show linea...
Complexity of Non-Adaptive Optimization Algorithms for a Class of Diffusions
Global optimization average-case complexity diffusion processes
2015/7/8
This paper is concerned with the analysis of the average error in approximating the global minimum of a 1-dimensional, time-homogeneous diffusion by non-adaptive methods. We derive the limiting distri...