Treffer: Subgradientní algoritmus pro konvexní optimalizační úlohy se stochastickým rozšířením

The aim of this thesis was to depict and analyze a subgradient algorithm for convex optimization problems and its stochastic extension with random subgradient sampling. The first part introduces gradient methods with exact line search for smooth convex functions. The second chapter extends these approaches to subgradient algorithms for nondifferentiable convex objective functions and includes proofs of convergence for both constant and diminishing step-size rules. The third part formulates the method's stochas- tic version and employs supermartingale analysis to prove almost sure convergence to the unique optimum. Numerical examples illustrate the trajectories of both the gradient and subgradient algorithms.