Related papers: Optimal Spectral Design with Prior Information

We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…

Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…

Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…

This paper studies the problem of reconstructing spectrally sparse signals from a small random subset of time domain samples via low-rank Hankel matrix completion with the aid of prior information. By leveraging the low-rank structure of…

An algorithm which computes a solution of a set optimization problem is provided. The graph of the objective map is assumed to be given by finitely many linear inequalities. A solution is understood to be a set of points in the domain…

Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…

In this paper, a spectral method based on conformal mappings is proposed to solve Steklov eigenvalue problems and their related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov…

We study the intrinsic limitations of sequential convex optimization through the lens of feedback information theory. In the oracle model of optimization, an algorithm queries an {\em oracle} for noisy information about the unknown…

We study the performance of the spectral method for the phase synchronization problem with additive Gaussian noises and incomplete data. The spectral method utilizes the leading eigenvector of the data matrix followed by a normalization…

We investigate the possibility of extending some results of Pazman and Pronzato (2014) to a larger set of optimality criteria. Namely, in a linear regression model the problem of computing D-, A-, E_k-optimal designs, of combining these…

We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…

Synthesis of optimization algorithms typically follows a {\em design-then-analyze\/} approach, which can obscure fundamental performance limits and hinder the systematic development of algorithms that operate near these limits. Recently, a…

This paper investigates recovery of an undamped spectrally sparse signal and its spectral components from a set of regularly spaced samples within the framework of spectral compressed sensing and super-resolution. We show that the existing…

Classifiers and rating scores are prone to implicitly codifying biases, which may be present in the training data, against protected classes (i.e., age, gender, or race). So it is important to understand how to design classifiers and scores…

We extend the result on the spectral projected gradient method by Birgin et al. in 2000 to a log-determinant semidefinite problem (SDP) with linear constraints and propose a spectral projected gradient method for the dual problem. Our…

We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…

We investigate an alternative solution method to the joint signal-beamformer optimization problem considered by Setlur and Rangaswamy[1]. First, we directly demonstrate that the problem, which minimizes the received noise, interference, and…

We propose a new constrained optimization approach to hyperspectral (HS) image restoration. Most existing methods restore a desirable HS image by solving some optimization problem, which consists of a regularization term(s) and a…

This paper addresses the design of input signals for the purpose of discriminating among a finite set of models dynamic systems within a given finite time interval. A motivating application is fault detection and isolation. We propose…

Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…