On a quadratic eigenproblem occurring in regularized total least squares
Computational Statistics & Data Analysis
A review of recent advances in global optimization
Journal of Global Optimization
Journal of Global Optimization
Regularized Total Least Squares: Computational Aspects and Error Bounds
SIAM Journal on Matrix Analysis and Applications
Efficient determination of the hyperparameter in regularized total least squares problems
Applied Numerical Mathematics
Large-scale Tikhonov regularization of total least squares
Journal of Computational and Applied Mathematics
Improved design of unimodular waveforms for MIMO radar
Multidimensional Systems and Signal Processing
Training Lp norm multiple kernel learning in the primal
Neural Networks
Hi-index | 0.00 |
We consider the problem of minimizing a fractional quadratic problem involving the ratio of two indefinite quadratic functions, subject to a two-sided quadratic form constraint. This formulation is motivated by the so-called regularized total least squares (RTLS) problem. A key difficulty with this problem is its nonconvexity, and all current known methods to solve it are guaranteed only to converge to a point satisfying first order necessary optimality conditions. We prove that a global optimal solution to this problem can be found by solving a sequence of very simple convex minimization problems parameterized by a single parameter. As a result, we derive an efficient algorithm that produces an $\epsilon$-global optimal solution in a computational effort of $O(n^3 \log \epsilon^{-1})$. The algorithm is tested on problems arising from the inverse Laplace transform and image deblurring. Comparison to other well-known RTLS solvers illustrates the attractiveness of our new method.