During recent decades, there have been a great number of research articles studying interior-point methods for solving problems in mathematical programming and constrained optimization. Stewart and O'Leary obtained an upper bound for scaled pseudoinverses sup W2P k(W 1 2 X) + W 1 2 k 2 of a matrix X where P is a set of diagonal positive deenite matrices. We improved their results to obtain the ...

A novel algorithm for source location by utilizing the time difference of arrival (TDOA) measurements of a signal received at spatially separated sensors is proposed. The algorithm is based on quadratic constraint total least-squares (QC-TLS) method and gives an explicit solution. The total least-squares method is a generalized data fitting method that is appropriate for cases when the system m...

Here, we give the detailed derivation of the dual problem of Eq. (2). First, we rewrite it as the following equivalent constrained optimization problem min 1 2 Z 2 F + λ W * s.t. Z = XW − Y (S1) Let us introduce the dual variable λP ∈ R n×m for the equality constraint, then the Lagrangian of Eq. (S1) can be written as L

In this paper we investigate the consistency of parameter estimates obtained from least squares identification with a quadratic parameter constraint. For generality, we consider infinite impulse response systems with colored input and output noise. In the case of finite data, we show that there always exists a possibly indefinite quadratic constraint depending on the noise realization that yiel...

Quadratic constraints on the weight vector of an adaptive linearly constrained minimum power (LCMP) beamformer can improve robustness to pointing errors and to random perturbations in sensor parameters. In this paper, we propose a technique for implementing a quadratic inequality constraint with recursive least squares (RLS) updating. A variable diagonal loading term is added at each step, wher...

This letter proposes a coregistration algorithm to compensate for the possible inaccuracy of trajectory sensor during synthetic aperture radar (SAR) image acquisition process. Such misalignment can be modeled as pure displacement in range and azimuth directions rotation effect due different angles sight. The approach is formalized constrained least squares (CLS) optimization problem enforcing c...

Constrained least squares is a ubiquitous optimization problem in machine learning, statistics, and signal processing. While projected gradient descent is usually an effective algorithm for solving constrained least squares at scale, the projection operator is often the computational bottleneck, especially for complicated constraints. To circumvent this limitation, we extend recent work on appr...