First-Order and Second-Order Conditions for Error Bounds
نویسندگان
چکیده
For a lower semicontinuous function f on a Banach space X, we study the existence of a positive scalar μ such that the distance function dS associated with the solution set S of f(x) ≤ 0 satisfies dS(x) ≤ μmax{f(x), 0} for each point x in a neighborhood of some point x0 in X with f(x) < for some 0 < ≤ +∞. We give several sufficient conditions for this in terms of an abstract subdifferential and the Dini derivatives of f . In a Hilbert space we further present some second-order conditions. We also establish the corresponding results for a system of inequalities, equalities, and an abstract constraint set.
منابع مشابه
An efficient numerical method for singularly perturbed second order ordinary differential equation
In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It ...
متن کاملSecond-Order Sufficient Conditions for Error Bounds in Banach Spaces
Recently, Huang and Ng presented second-order sufficient conditions for error bounds of continuous and Gâteaux differentiable functions in Banach spaces. Wu and Ye dropped the assumption of Huang and Ng on Gâteaux differentiability but required the space to be a Hilbert space. We carry on this research in two directions. First we extend Wu and Ye’s result to some non-Hilbert spaces; second, sam...
متن کاملOn Long Time Error Bounds for the Wave Equation on Second Order Form
Temporal error bounds for the wave equation expressed on second order form are investigated. We show that, with appropriate choices of boundary conditions, the time and space derivatives of the error are bounded even for long times. No long time bound on the error itself is obtained, although numerical experiments indicate that a bound exists.
متن کاملA Comparative Solution of Natural Convection in an Open Cavity using Different Boundary Conditions via Lattice Boltzmann Method
A Lattice Boltzmann method is applied to demonstrate the comparison results of simulating natural convection in an open end cavity using different hydrodynamic and thermal boundary conditions. The Prandtl number in the present simulation is 0.71, Rayleigh numbers are 104,105 and 106 and viscosities are selected 0.02 and 0.05. On-Grid bounce-back method with first-order accuracy and non-slip met...
متن کاملPerformance Bounds for Morse's Dynamic Certainty Equivalence Adaptive Controllert
In this paper we consider a model reference adaptive control scheme where the classical error augmentation and standard tuning error normalirat.ion are avoided through the use of Morse's high order tuner. We consider the particular scheme of Morse where the concept of dynamic certainty equivalence is used to reduce the error equation to one that involves only first order dynamics. With such an ...
متن کاملUniform Approximation by Neural Networks Activated by First and Second Order Ridge Splines
We establish sup-norm error bounds for functions that are approximated by linear combinations of first and second order ridge splines and show that these bounds are near-optimal.
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 14 شماره
صفحات -
تاریخ انتشار 2004