We present a new algorithmic framework for solving unconstrained minimization problems that incorporates a curvilinear linesearch. The search direction used in our framework is a combination of an approximate Newton direction and a direction of negative curvature. Global convergence to a stationary point where the Hessian matrix is positive semideenite is exhibited for this class of algorithms ...

The main goal of this paper is to analyze the behavior of nonmonotone hybrid tabu search approaches when solving systems of nonlinear inequalities and equalities through the global optimization of an appropriate merit function. The algorithm combines global and local searches and uses a nonmonotone reduction of the merit function to choose the local search. Relaxing the condition aims to call t...

In this paper, a modified BFGS algorithm is proposed for unconstrained optimization. The proposed algorithm has the following properties: (i) a nonmonotone line search technique is used to obtain the step size [Formula: see text] to improve the effectiveness of the algorithm; (ii) the algorithm possesses not only global convergence but also superlinear convergence for generally convex functions...

The limited memory BFGS (L-BFGS) method is one of the popular methods for solving large-scale unconstrained optimization. Since standard L-BFGS uses a line search to guarantee its global convergence, it sometimes requires large number function evaluations. To overcome difficulty, we propose new with certain regularization technique. We show convergence under usual assumptions. In order make mor...

Here we present a primal-dual interior point nonmonotone line search filter method for nonlinear programming. The filter relies on three measures, the feasibility, the complementarity and the optimality presented in the optimality conditions, considers relaxed acceptability criteria for the step size and includes a feasibility restoration phase. The evaluation of the method is until now made on...

In our paper, we present a sparse quasi-Newton method, called the direct Broyden for solving nonlinear equations. The method can be seen as Broyden-like and is least change update satisfying sparsity condition tangent simultaneously. local q-superlinear convergence presented based on bounded deterioration property Dennis–Moré condition. By adopting nonmonotone line search, establish global supe...

In this paper, we propose a variable metric method for unconstrained multiobjective optimization problems (MOPs). First, sequence of points is generated using different positive definite matrices in the generic framework. It proved that accumulation are Pareto critical points. Then, without convexity assumption, strong convergence established proposed method. Moreover, use common matrix to appr...