| In this paper, an alternating direction method with Gaussian back substitution (G-ADM) for a type of inverse quadratic programming problem is discussed, where vector l1-norm and matrix nuclear norm are contained in objective function. In the inverse problem, the parameters in the objective function of a given quadratic programming (QP) problem are adjusted as little as possible in the sense of matrix nuclear norm and vector l1-norm so that a known feasible solution which is obtained by experience or experiments becomes the optimal one. One can formulate this problem as a constrained minimization problem with a separable objective function. Then lin-earized alternating direction method (ADM) in sense of the customized proximal point algorithm (PPA) and semi-smooth Newton method are employed for solving sub-problems. Convergence analysis is established and Matlab codes are made to test this type of inverse problem.The main results of this dissertation are summarized as follows:1. Chapter1gives the background and current research of inverse optimization. Then we describe the model of inverse QP problems studied in this thesis, and derive a constrained mini-mization problem with a separable objective function.2. Matrix and nonsmooth analysis related preliminaries are given in Chapter2, in which projection on positive semi-definite cone, Moreau-Yosida regularization related knowledge, NCP function and so on are contained.3. In Chapter3, after introducing ADM related knowledge, the G-ADM for this inverse problem is presented. For solving sub-problems, linearized ADM in sense of the customized PPA and semi-smooth Newton method are employed.4. Convergence analysis is established in Chapter4. convergence theorem shows that the sequence generated by the proposed algorithm converges to the solution point.5. In Chapter5, we report the numerical results, which show that the proposed method is practical for this type of inverse QP problem. |
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