Summary.
Many interesting and important constrained optimization problems in mathematical programming can be translated into an equivalent linear projection equation\( u = P_{\Omega} [ u - (Mu+q)] . \) Here, \(P_{\Omega}(\cdot)\) is the orthogonal projection on some convex set\(\Omega\) (e.g. \(\Omega= {\Bbb R}^n_+\)) and \(M\) is a positive semidefinite matrix. This paper presents some new methods for solving a class of linear projection equations. The search directions of these methods are straighforward extensions of the directions in traditional methods for unconstrained optimization. Based on the idea of a projection and contraction method [7] we get a simple step length rule and are able to obtain global linear convergence.
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Received April 19, 1993 / Revised version received February 9, 1994
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He, B. Solving a class of linear projection equations . Numer. Math. 68, 71–80 (1994). https://doi.org/10.1007/s002110050048
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DOI: https://doi.org/10.1007/s002110050048