A Trust Region Interior Point Algorithm for Linearly Constrained Optimization
نویسندگان
چکیده
We present an extension, for nonlinear optimization under linear constraints, of an algorithm for quadratic programming using a trust region idea introduced by Ye and Tse [Math. Programming, 44 (1989), pp. 157–179] and extended by Bonnans and Bouhtou [RAIRO Rech. Opér., 29 (1995), pp. 195–217]. Due to the nonlinearity of the cost, we use a linesearch in order to reduce the step if necessary. We prove that, under suitable hypotheses, the algorithm converges to a point satisfying the first-order optimality system, and we analyze under which conditions the unit stepsize will be asymptotically accepted.
منابع مشابه
Optimality condition and complexity analysis for linearly-constrained optimization without differentiability on the boundary
In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By exploiting an interior point technique, we present firstand second-order optimality conditions for this problem that reduces to classical ones when the derivative on the boundary is available. For this type of problems,...
متن کاملA Primal-Infeasible Interior Point Algorithm For Linearly Constrained Convex Programming
In the paper a primal-infeasible interior point algorithm is proposed for linearly constrained convex programming. The starting point is any positive primal-infeasible dual-feasible point in a large region. The method maintains positivity of the iterates which point satisfies primalinfeasible dual-feasible point. At each iterates it requires to solve approximately a nonlinear system. It is show...
متن کاملConvergent Infeasible Interior-Point Trust-Region Methods for Constrained Minimization
We study an infeasible interior-point trust-region method for constrained minimization. This method uses a logarithmic-barrier function for the slack variables and updates the slack variables using second-order correction. We show that if a certain set containing the iterates is bounded and the origin is not in the convex hull of the nearly active constraint gradients everywhere on this set, th...
متن کاملMethods for Nonlinear Constraints in Optimization Calculations
Ten years ago, the broad consensus among researchers in constrained optimization was that sequential quadratic programming (SQP) methods were the methods of choice. While, in the long term, this position may be justiied, the past ten years have exposed a number of diiculties with the SQP approach. Moreover, alternative methods have shown themselves capable of solving large-scale problems. In th...
متن کاملSolving the Unconstrained Optimization Problems Using the Combination of Nonmonotone Trust Region Algorithm and Filter Technique
In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems that is equipped with the filter technique. In the proposed method, the various nonmonotone technique is used. Using this technique, the algorithm can advantage from nonmonotone properties and it can increase the rate of solving the problems. Also, the filter that is used in...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM Journal on Optimization
دوره 7 شماره
صفحات -
تاریخ انتشار 1997