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 W∈P ‖(W 12X)+W 2 ‖2 of a matrix X where P is a set of diagonal positive definite matrices. We improved their results to obtain the suprem...

Abstract. In this paper, we investigate the numerical identifications of physical parameters in parabolic initial-boundary value problems. The identifying problem is first formulated as a constrained minimization one using the output least squares approach with the H 1-regularization or BV -regularization. Then a simple finite element method is used to approximate the constrained minimization p...

The following is a brief review of least squares optimization and constrained optimization techniques, which are widely used to analyze and visualize data. Least squares (LS) optimization problems are those in which the objective (error) function is a quadratic function of the parameter(s) being optimized. The solutions to such problems may be computed analytically using the tools of linear alg...

In system identification, the true system is often known to be stable. However, due to finite sample constraints, modeling errors, plant disturbances and measurement noise, the identified model may be unstable. We present a constrained optimization method to ensure asymptotic stability of the identified model in the context of subspace identification methods. In subspace identification, we firs...

The box-constrained integer least squares problem (BILS) arises in MIMO wireless communications applications. Typically a sphere decoding algorithm (a tree search algorithm) is used to solve the problem. In order to make the search algorithm more efficient, the columns of the channel matrix in the BILS problem have to be reordered. To our knowledge, there are currently two algorithms for column...

January 28, 2000 Abstract. This paper investigates quasi-Newton updates for equality-constrained optimization. Using a least-change argument we derive a class of rank-3 updates to approximations of the one-sided projection of the Hessian of the Lagrangian which keeps the appropriate part symmetric (and possibly positive definite). By imposing the usual assumptions we are able to prove 1-step su...

In this paper, a novel algorithm for image restoration is proposed based on constrained total least-squares (CTLS) estimation, that is, adaptively regularized CTLS (ARCTLS). It is well known that in the regularized CTLS (RCTLS) method, selecting a proper regularization parameter is very difficult. For solving this problem, we take the first-order partial derivative of the classic equation of RC...

In this paper a modification of the standard algorithm for non-negativity-constrained linear least squares regression is proposed. The algorithm is specifically designed for use in multiway decomposition methods such as PARAFAC and N-mode principal component analysis. In those methods the typical situation is that there is a high ratio between the numbers of objects and variables in the regress...

Abstract. One of the fundamental problems in electronic structure calculations is to determine the electron density associated with the minimum total energy of a molecular or bulk system. The total energy minimization problem is often formulated as a nonlinear eigenvalue problem. The most widely used algorithm for solving this type of problem is the self-consistent field (SCF) iteration acceler...

In this short paper we present an improved computational technique to solve the Fredholm integral equation of the first kind which arises in image restoration and other inverse filtering applications. The technique is based on the works of Phillips, Twomey, and Hunt. We show that when the integral represents a convolution, the integral equation can be solved iteratively with each iteration requ...