牛顿法的限制:传统的牛顿法在优化理论中非常强大,特别是在寻找函数局部最小值时。然而,牛顿法有几个限制,最主要的是它依赖于Hessian矩阵(二阶导数矩阵)的逆,这在Hessian矩阵接近奇异或不定时可能导致算法不稳定或不收敛。 更好的全局收敛保证:虽然牛顿法在局部表现良好,但它通常缺乏全局收敛性。这意味着,如果初始点...
Cubic Regularized Newton基本性质这一文章介绍了Cubic Newton的基本性质。接下来将介绍其全局收敛性及其证明,首先简单回顾之前提过的公式。 (1)TM(x)∈Argminy[⟨f′(x),y−x⟩+12⟨f″(x)(y−x),y−x⟩+M6‖y−x‖3]. (2)‖f′(TM(x))‖≤12(L+M)rM2(x). (3)ifM≥L,f...
The cubic regularization (CR) algorithm has attracted a lot of attentions in the literature in recent years. We propose a new reformulation of the cubic regularization subproblem. The reformulation is an unconstrained convex problem that requires computing the minimum eigenvalue of the Hessian. Then ...
On the use of iterative methods in cubic regularization for unconstrained optimization. Comput. Optim. Appl., 60(1):35-57, 2014.Bianconcini, T., Liuzzi, G., Morini, B., Sciandrone, M.: On the use of iterative methods in cubic regularization for unconstrained optimization. Comput. Optim...
An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity A local convergence analysis of Newton's method for finding a singularity of a differentiable vector field defined on a complete Riemannian manifold, based... C Cartis,NIM...
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model uses the framework of cubic regularization of Newton's ...
Second, being the spline intrinsically a smooth 1D resistivity depth profile, there is no need of solution regularization. An example of application of this approach to MT single site data from a geothermal field is presented, and a comparison with blocky and smoothed models and data from a ...
40 Bregman divergence regularization of optimal transport problems on a finite set 57:24 The principal Chebotarev density theorem 50:59 Understanding form and function in vascular tumours 54:28 A construction of Bowen-Margulis measure (Main talk) 55:52 A construction of Bowen-Margulis measure (...
摘要: A finite-dimensional regularization method to solve a discrete Fredholm integral equation of the first kind typical of EXAFS spectroscopy is presented. Numerical experiments are reported to illustrate the effectiveness of the method.DOI: http://dx.doi.org/ ...
We consider the application of Tikhonov type regularization methods for computing a cubic spline approximation to the solution of a particular Fredholm integral equation of the first kind which arises in laser Doppler anemometry experiments. The method of generalized cross validation is used to calculate...