An improved subgradient method for constrained nondifferentiable optimization

Approximate Primal Solutions and Rate Analysis for Dual Subgradient Methods

In this paper, we study methods for generating approximate primal solutions as a by-product of subgradient methods applied to the Lagrangian dual of a primal convex (possibly nondifferentiable) constrained optimization problem. Our work is motivated by constrained primal problems with a favorable dual problem structure that leads to efficient implementation of dual subgradient methods, such as ...

Multiple Cuts in Separating Plane Algorithms

This paper presents an extended version of the separation plane algorithms for subgradientbased finite-dimensional nondifferentiable convex blackbox optimization. The extension introduces additional cuts for epigraph of the conjugate of objective function which improve the convergence of the algorithm. The case of affine cuts is considered in more details and it is shown that it requires soluti...

Inexact subgradient methods for quasi-convex optimization problems

In this paper, we consider a generic inexact subgradient algorithm to solve a nondifferentiable quasi-convex constrained optimization problem. The inexactness stems from computation errors and noise, which come from practical considerations and applications. Assuming that the computational errors and noise are deterministic and bounded, we study the effect of the inexactness on the subgradient ...

Nondifferentiable Optimization with Epsilon Subgradient Methods

Nondifferentiable Optimization via Approximation*

Optimization problems with nondifferentiable cost functionals, particularly minimax problems, have received considerable attention recently since they arise naturally in a variety of contexts. Optimality conditions for such problems have been derived by several authors while a number of computational methods have been proposed for their solution (the reader is referred to [1] for:a fairly compl...