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In this paper, we present a QP-free algorithm without a penalty function or a filter for nonlinear general-constrained optimization. At each iteration, three systems of linear equations with the same coefficient matrix are solved to yield search direction; the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced. There is no feasibility restoration phase in our algorithm, which is necessary for filter methods. The algorithm possesses global convergence as well as superlinear convergence under some mild conditions including a weaker assumption of positive definiteness. Finally, some preliminary numerical results are reported. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the Polak–Ribière (or Polak–Ribière plus) conjugate gradient method for solving optimality condition of an unconstrained minimization problem. We give two new steplength rules only using gradient, and under gradient-Lipschitz assumption prove this method’s global convergence correspondingly. Then, we develop a practical Polak–Ribière plus method whose steplength is located by one inequality only using gradient, and report promising numerical results on high accuracy solution for some standard test problems when compared to the state-of-art methods in this research direction. Importantly, our work provides a new idea of devising a practical version of the celebrated Polak–Ribière (or Polak–Ribière plus) method. [Copyright &y& Elsevier]

Abstract: Conjugate gradient methods have been paid attention to, because they can be directly applied to large-scale unconstrained optimization problems. In order to incorporate second order information of the objective function into conjugate gradient methods, Dai and Liao (2001) proposed a conjugate gradient method based on the secant condition. However, their method does not necessarily generate a descent search direction. On the other hand, Hager and Zhang (2005) proposed another conjugate gradient method which always generates a descent search direction. In this paper, combining Dai–Liao’s idea and Hager–Zhang’s idea, we propose conjugate gradient methods based on secant conditions that generate descent search directions. In addition, we prove global convergence properties of the proposed methods. Finally, preliminary numerical results are given. [Copyright &y& Elsevier]

Abstract: Nonlinear conjugate gradient (CG) methods have played an important role in solving large-scale unconstrained optimization. Their wide application in many fields is due to their low memory requirements and global convergence properties. Numerous studies and modifications have been conducted recently to improve this method. In this paper, a new class of conjugate gradient coefficients (βk ) that possess global convergence properties is presented. The global convergence result is established using exact line searches. Numerical result shows that the proposed formula is superior and more efficient when compared to other CG coefficients. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a new penalty-free-type method for nonlinear equality constrained problems. The new algorithm uses trust region framework and feasibility safeguarding technique. Moreover, it has no choice of penalty parameter and penalty function as a merit function, and it does not use the filter technique to avoid the penalty function either. We analyze the global convergence of the main algorithm under the standard assumptions. The preliminary numerical tests are reported. [Copyright &y& Elsevier]

Abstract: In this paper, we combine the filter technique with a modified sequential quadratic programming (SQP) method. The optimization solution is obtained by reducing step length, which is obtained by an exact linear search. Furthermore, this method can start with an infeasible initial point. The method uses a filter to promote global convergence. [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, by means of an active set strategy, we present a projected spectral gradient algorithm for solving large-scale bound constrained optimization problems. A nice property of the active set estimation technique is that it can identify the active set at the optimal point without requiring strict complementary condition, which is potentially used to solve degenerated optimization problems. Under appropriate conditions, we show that this proposed method is globally convergent. We also do some numerical experiments by using some bound constrained problems from CUTEr library. The numerical comparisons with SPG, TRON, and L-BFGS-B show that the proposed method is effective and promising. [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]

Abstract: In this paper, based on a simple model of the trust region subproblem, we propose a new self-adaptive trust region method with a line search technique for solving unconstrained optimization problems. By use of the simple subproblem model, the new method needs less memory capacitance and computational complexity. And the trust region radius is adjusted with a new self-adaptive adjustment strategy which makes full use of the information at the current point. When the trial step results in an increase in the objective function, the method does not resolve the subproblem, but it performs a line search technique from the failed point. Convergence properties of the method are proved under certain conditions. Numerical experiments show that the new method is effective and attractive for large-scale optimization problems. [Copyright &y& Elsevier]