We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [1] by taking a different perspective, leading to an algorithm which is conceptually more natural, has notably improved convergence rates, and for which the analysis is surprisingly simple. At ...

The efficiency of the network flow techniques can be exploited in the solution of nonlinearly constrained network flow problems by means of approximate subgradient methods. In particular, we consider the case where the side constraints (non-network constraints) are convex. We propose to solve the dual problem by using &-subgradient methods given that the dual function is estimated by minimizing...

Lagrangean dualization and subgradient optimization techniques are frequently used within the field of computational optimization for finding approximate solutions to large, structured optimization problems. The dual subgradient scheme does not automatically produce primal feasible solutions; there is an abundance of techniques for computing such solutions (via penalty functions, tangential app...

Simultaneous subgradient projection algorithms for the convex feasibility problem use subgradient calculations and converge sometimes even in the inconsistent case. We devise an algorithm that uses seminorm-induced oblique projections onto super half-spaces of the convex sets, which is advantageous when the subgradient-Jacobian is a sparse matrix at many iteration points of the algorithm. Using...

Subgradient methods are popular tools for nonsmooth, convex minimization , especially in the context of Lagrangean relaxation; their simplicity has been a main contribution to their success. As a consequence of the nonsmoothness, it is not straightforward to monitor the progress of a subgradient method in terms of the approximate fulllment of optimality conditions, since the subgradients used i...

Block coordinate descent methods and stochastic subgradient methods have been extensively studied in optimization and machine learning. By combining randomized block sampling with stochastic subgradient methods based on dual averaging ([22, 36]), we present stochastic block dual averaging (SBDA)—a novel class of block subgradient methods for convex nonsmooth and stochastic optimization. SBDA re...