Journal
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Volume 28, Issue 2, Pages 425-445Publisher
SIAM PUBLICATIONS
DOI: 10.1137/040616851
Keywords
regularized total least squares; fractional programming; nonconvex quadratic optimization; convex programming
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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.
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