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A novel filled function method is suggested for solving box-constrained systems of nonlinear equations. Firstly, the original problem is converted into an equivalent global optimization problem. Subsequently, a novel filled function with one parameter is proposed for solving the converted global optimization problem. Some properties of the filled function are studied and discussed. Finally, an algorithm based on the proposed novel filled function for solving systems of nonlinear equations is presented. The objective function value can be reduced by quarter in each iteration of our algorithm. The implementation of the algorithm on several test problems is reported with satisfactory numerical results. [ABSTRACT FROM AUTHOR]

A practical algorithm for solving large-scale box-constrained optimization problems is developed, analyzed, and tested. In the proposed algorithm, an identification strategy is involved to estimate the active set at per-iteration. The components of inactive variables are determined by the steepest descent method at first finite number of steps and then by conjugate gradient method subsequently. Under some appropriate conditions, we show that the algorithm converges globally. Numerical experiments and comparisons by using some box-constrained problems from CUTEr library are reported. Numerical comparisons illustrate that the proposed method is promising and competitive with the well-known method--L-BFGS-B. [ABSTRACT FROM AUTHOR]

A modified parallel variable distribution (PVD) algorithm for solving large-scale constrained optimization problems is developed, which modifies quadratic subproblem QP1 at each iteration instead of the QP01 of the SQP-type PVD algorithm proposed by C. A. Sagastiz'abal and M. V. Solodov in 2002.The algorithm can circumvent the difficulties associated with the possible inconsistency of QP01 subproblem of the original SQP method. Moreover, we introduce a nonmonotone technique instead of the penalty function to carry out the line search procedure with more flexibly. Under appropriate conditions, the global convergence of the method is established. In the final part, parallel numerical experiments are implemented on CUDA based on GPU (Graphics Processing unit). [ABSTRACT FROM AUTHOR]

Motivated by the method of Su and Pu (2009), we present an improved nonmonotone filter trust region algorithm for solving nonlinear equality constrained optimization. In our algorithmamodified nonmonotone filter technique is proposed and the restoration phase is not needed. At every iteration, in common with the composite-step SQP methods, the step is viewed as the sum of two distinct components, a quasinormal step and a tangential step. Amore relaxed accepted condition for trial step is given and a crucial criterion is weakened. Under some suitable conditions, the global convergence is established. In the end, numerical results show our method is effective. [ABSTRACT FROM AUTHOR]