In solving a mathematical program, the exact evaluation of the objective function and its subgradients can be computationally burdensome. For example, in a stochastic program, the objective function is typically defined through a multi-dimensional integration. Solution procedures for stochastic programs are usually based on functional approximation techniques, or statistical applications of subgradient methods. In this dissertation, we explore algorithms by combining functional approximation techniques with subgradient optimization methods. This class of algorithms is referred to as "inexact subgradient methods". First, we develop a basic inexact subgradient method and identify conditions under which this approach will lead to an optimal so...
Traditionally, stochastic approximation (SA) schemes have been popular choices for solving stochasti...
Two topics are addressed. The first refers to the numerical computation of integrals and expected va...
When non-smooth, convex minimization problems are solved by subgradient optimization methods, the su...
Subgradient methods for nondifferentiable optimization benefit from deflection, i.e., defining the s...
Subgradient methods for constrained nondifferentiable problems benefit from projection of the search...
The subgradient method is both a heavily employed and widely studied algorithm for non-differentiabl...
The subgradient method is both a heavily employed and widely studied algorithm for non-differentiabl...
Subgradient methods (SM) have long been the preferred way to solve the large-scale Nondifferentiable...
Subgradient methods (SM) have long been the preferred way to solve the large-scale Nondifferentiable...
The topic of the thesis is subgradient optimization methods in convex, nonsmooth optimization. These...
International audienceWe discuss non-Euclidean stochastic approximation algorithms for optimization ...
Separable sublinear functions are used to provide upper bounds on the recourse function of a stochas...
In this article, we consider convergence properties of the normalized subgradient method which emplo...
In this article, we consider convergence properties of the normalized subgradient method which emplo...
Traditionally, stochastic approximation (SA) schemes have been popular choices for solving stochasti...
Traditionally, stochastic approximation (SA) schemes have been popular choices for solving stochasti...
Two topics are addressed. The first refers to the numerical computation of integrals and expected va...
When non-smooth, convex minimization problems are solved by subgradient optimization methods, the su...
Subgradient methods for nondifferentiable optimization benefit from deflection, i.e., defining the s...
Subgradient methods for constrained nondifferentiable problems benefit from projection of the search...
The subgradient method is both a heavily employed and widely studied algorithm for non-differentiabl...
The subgradient method is both a heavily employed and widely studied algorithm for non-differentiabl...
Subgradient methods (SM) have long been the preferred way to solve the large-scale Nondifferentiable...
Subgradient methods (SM) have long been the preferred way to solve the large-scale Nondifferentiable...
The topic of the thesis is subgradient optimization methods in convex, nonsmooth optimization. These...
International audienceWe discuss non-Euclidean stochastic approximation algorithms for optimization ...
Separable sublinear functions are used to provide upper bounds on the recourse function of a stochas...
In this article, we consider convergence properties of the normalized subgradient method which emplo...
In this article, we consider convergence properties of the normalized subgradient method which emplo...
Traditionally, stochastic approximation (SA) schemes have been popular choices for solving stochasti...
Traditionally, stochastic approximation (SA) schemes have been popular choices for solving stochasti...
Two topics are addressed. The first refers to the numerical computation of integrals and expected va...
When non-smooth, convex minimization problems are solved by subgradient optimization methods, the su...