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Abstract: We present a class of trust region algorithms that do not use any penalty function or a filter for nonlinear equality constrained optimization. In each iteration, the infeasibility is controlled by a progressively decreasing upper limit and trial steps are computed by a Byrd–Omojokun-type trust region strategy. Measures of optimality and infeasibility are computed, whose relationship serves as a criterion on which the algorithm decides which one to focus on improving. As a result, the algorithm keeps a balance between the improvements on optimality and feasibility even if no restoration phase which is required by filter methods is used. The framework of the algorithm ensures the global convergence without assuming regularity or boundedness on the iterative sequence. By using a second order correction strategy, Marato’s effect is avoided and fast local convergence is shown. The preliminary numerical results are reported. [Copyright &y& Elsevier]

Abstract: In this paper, an active set limited BFGS algorithm is proposed for bound constrained optimization. The global convergence will be established under some suitable conditions. Numerical results show that the given method is effective. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a trust region method for unconstrained optimization that can be regarded as a combination of conic model, nonmonotone and line search techniques. Unlike in traditional trust region methods, the subproblem of our algorithm is the conic minimization subproblem; moreover, our algorithm performs a nonmonotone line search to find the next iteration point when a trial step is not accepted, instead of resolving the subproblem. The global and superlinear convergence results for the algorithm are established under reasonable assumptions. Numerical results show that the new method is efficient for unconstrained optimization problems. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a new feasible primal–dual interior point algorithm for solving inequality constrained optimization problems is presented. At each iteration, the algorithm solves only two or three reduced systems of linear equations with the same coefficient matrix. The searching direction is feasible and the object function is monotone decreasing. The proposed algorithm is proved to possess global and superlinear convergence under mild conditions. Finally, some numerical experiments with the algorithm are reported. [Copyright &y& Elsevier]