Search

Traditional inexact SQP algorithm can only solve equality constrained optimization (Byrd et al. Math. Program. 122, 273-299 2010). In this paper, we propose a new inexact SQP algorithm with affine scaling technique for nonlinear systems of mixed equalities and inequalities, which arise in complementarity and variational inequalities. The nonlinear systems are transformed into a special nonlinear optimization with equality and bound constraints, and then we give a new inexact SQP algorithm for solving it. The new algorithm equipped with affine scaling technique does not require a quadratic programming subproblem with inequality constraints. The search direction is computed by solving one linear system approximately using iterative linear algebra techniques. Under mild assumptions, we discuss the global convergence. The preliminary numerical results show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes an affine scaling trust-region method with line search filter technique for solving nonlinear optimization problems subject to bounds on variables. At the current iteration, the trial step is generated by the general trust-region subproblem which is defined by minimizing a quadratic function subject only to an affine scaling ellipsoidal constraint. Both trust-region strategy and line search filter technique will switch to trail backtracking step which is strictly feasible. Meanwhile, the proposed method does not depend on any external restoration procedure used in line search filter technique. A new backtracking relevance condition is given which is weaker than the switching condition to obtain the global convergence of the algorithm. The global convergence and fast local convergence rate of this algorithm are established under reasonable assumptions. Preliminary numerical results are reported indicating the practical viability and show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose conjugate gradient path method for solving derivative-free unconstrained optimization. The iterative direction is obtained by constructing and solving quadratic interpolation model of the objective function with conjugate gradient methods. The global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, the numerical results are reported to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The authors propose a dwindling filter algorithm with Zhou's modified subproblem for nonlinear inequality constrained optimization. The feasibility restoration phase, which is always used in the traditional filter method, is not needed. Under mild conditions, global convergence and local superlinear convergence rates are obtained. Numerical results demonstrate that the new algorithm is effective. [ABSTRACT FROM AUTHOR]

In this paper, we propose a non-monotone line search multidimensional filter-SQP method for general nonlinear programming based on the Wächter-Biegler methods for nonlinear equality constrained programming. Under mild conditions, the global convergence of the new method is proved. Furthermore, with the non-monotone technique and second order correction step, it is shown that the proposed method does not suffer from the Maratos effect, so that fast local convergence to second order sufficient local solutions is achieved. Numerical results show that the new approach is efficient. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new trust-region-projected Hessian algorithm with nonmonotonic backtracking interior point technique for linear constrained optimization. By performing the QR decomposition of an affine scaling equality constraint matrix, the conducted subproblem in the algorithm is changed into the general trust-region subproblem defined by minimizing a quadratic function subject only to an ellipsoidal constraint. By using both the trust-region strategy and the line-search technique, each iteration switches to a backtracking interior point step generated by the trustregion subproblem. The global convergence and fast local convergence rates for the proposed algorithm are established under some reasonable assumptions. A nonmonotonic criterion is used to speed up the convergence in some ill-conditioned cases. [ABSTRACT FROM AUTHOR]