Sample average approximations of strongly convex stochastic programs in Hilbert spaces

نویسندگان

چکیده

Abstract We analyze the tail behavior of solutions to sample average approximations (SAAs) stochastic programs posed in Hilbert spaces. require that integrand be strongly convex with same convexity parameter for each realization. Combined a standard condition from literature on programming, we establish non-asymptotic exponential bounds distance between SAA and program’s solution, without assuming compactness feasible set. Our assumptions are verified class infinite-dimensional optimization problems governed by affine-linear partial differential equations random inputs. present numerical results illustrating our theoretical findings.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On sample size control in sample average approximations for solving smooth stochastic programs

We consider smooth stochastic programs and develop a discrete-time optimal-control problem for adaptively selecting sample sizes in a class of algorithms based on sample average approximations (SAA). The control problem aims to minimize the expected computational cost to obtain a near-optimal solution of a stochastic program and is solved approximately using dynamic programming. The optimal-con...

متن کامل

Variance reduction in sample approximations of stochastic programs

This paper studies the use of randomized Quasi-Monte Carlo methods (RQMC) in sample approximations of stochastic programs. In high dimensional numerical integration, RQMC methods often substantially reduce the variance of sample approximations compared to MC. It seems thus natural to use RQMC methods in sample approximations of stochastic programs. It is shown, that RQMC methods produce epi-con...

متن کامل

Stochastic Variational Inequalities: Residual Minimization Smoothing Sample Average Approximations

Abstract. The stochastic variational inequality (SVI) has been used widely, in engineering and economics, as an effective mathematical model for a number of equilibrium problems involving uncertain data. This paper presents a new expected residual minimization (ERM) formulation for a class of SVI. The objective of the ERM-formulation is Lipschitz continuous and semismooth which helps us guarant...

متن کامل

Stochastic Processes with Sample Paths in Reproducing Kernel Hilbert Spaces

A theorem of M. F. Driscoll says that, under certain restrictions, the probability that a given Gaussian process has its sample paths almost surely in a given reproducing kernel Hilbert space (RKHS) is either 0 or 1. Driscoll also found a necessary and sufficient condition for that probability to be 1. Doing away with Driscoll’s restrictions, R. Fortet generalized his condition and named it nuc...

متن کامل

Stochastic differential inclusions of semimonotone type in Hilbert spaces

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Optimization Letters

سال: 2022

ISSN: ['1862-4480', '1862-4472']

DOI: https://doi.org/10.1007/s11590-022-01888-4