Abstract: In this paper, we introduce a vector-valued Tikhonov-type regularization algorithm for an extended-valued multiobjective optimization problem. Under some mild conditions, we prove that any sequence generated by this algorithm converges to a weak Pareto optimal solution of the multiobjective optimization problem. Our results improve and generalize some known results. [Copyright &y& Elsevier]
Abstract: This paper presents an affine scaling optimal path approach in association with nonmonotonic interior backtracking line search technique for nonlinear optimization subject to linear constraints. We shall employ the eigensystem decomposition and affine scaling mapping to form affine scaling optimal curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The nonmonotone criterion is used to speed up the convergence progress in the contours of objective function with large curvature. Theoretical analysis is given which prove that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable conditions. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]
Abstract: This paper studies a successive partitioning group correction algorithm and its some modified algorithms for solving large scale sparse unconstrained optimization problems. The methods depend on a symmetric consistent partition of the columns of the Hessian matrix. A q-superlinear convergence result and an r-convergence rate estimate show that the methods have good local convergence properties. The numerical results show that the methods, especially the modified algorithms, may be competitive with some current used algorithms. [Copyright &y& Elsevier]