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An augmented Lagrangian method for a class of Inverse quadratic programming problems. (English) Zbl 1201.90152
The article considers an inverse quadratic optimization problem in which the coefficients of a quadratic objective function are adjusted as little as possible so that a known feasible solution becomes optimal. The problem is formulated as a minimization problem with a positive semidefinite cone constraint. Its dual is a linearly constrained semismoothly differentiable convex optimization problem with fewer variables than the original one.
Global convergence of the augmented Lagrangian method for the dual problem is demonstrated, and convergence rates for primal and dual iterates are established. As the objective function of the dual problem is only semismoothly differentiable, the analysis requires extensive tools. The semismooth Newton method with Armijo line search is applied to solve the subproblems in the augmented Lagrange approach, which is proven to have global convergence and local quadratic rate. Numerical results illustrate the performance of the proposed method.

90C22 Semidefinite programming
90C31 Sensitivity, stability, parametric optimization
90C20 Quadratic programming
49M29 Numerical methods involving duality
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