We propose a new nonmonotone filter method to promote global and fast local convergence for sequential quadratic programming algorithms. Our method uses two filters: a global gfilter for global convergence, and a local nonmonotone l-filter that allows us to establish fast local convergence. We show how to switch between the two filters efficiently, and we prove global and superlinear local conv...

In this paper, we propose a modified trust-region filter method algorithm for Minimax problems, which based on the framework of SQP-filter method and associated with the technique of nonmonotone method. We use the SQP subproblem to acquire an attempt step, and use the filter to weigh the effect of the attempt step so as to avoid using penalty function. The algorithm uses the Lagrange function a...

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We propose a limited memory steepest descent method for solving unconstrained optimization problems. As a steepest descent method, the step computation in each iteration only requires the evaluation of a gradient of the objective function and the calculation of a scalar stepsize. When employed to solve certain convex problems, our method reduces to a variant of the limited memory steepest desce...

This paper considers optimization problems on the Stiefel manifold XX = Ip, where X ∈ Rn×p is the variable and Ip is the p-by-p identity matrix. A framework of constraint preserving update schemes is proposed by decomposing each feasible point into the range space of X and the null space of X. While this general framework can unify many existing schemes, a new update scheme with low complexity ...

Linearly constrained optimization problems with simple bounds are considered in the present work. First, a preconditioned spectral gradient method is defined for the case in which no simple bounds are present. This algorithm can be viewed as a quasiNewton method in which the approximate Hessians satisfy a weak secant equation. The spectral choice of steplength is embedded into the Hessian appro...

using a simple quadratic model in the trust region subproblem, a new adaptive nonmonotone trust region method is proposed for solving unconstrained optimization problems. in our method, based on a slight modification of the proposed approach in (j. optim. theory appl. 158(2):626-635, 2013), a new scalar approximation of the hessian at the current point is provided. our new proposed method is eq...