Submodularity is a well-known concept in integer programming and combinatorial optimization. Submodular set functions capture the diminishing returns phenomenon, which has wide-ranging applications in various domains. Typically, a submodular set function models the utility of homogenous items selected from a single ground set. Selecting an item or not is naturally...
In this thesis, we aim to develop efficient algorithms with theoretical guarantees for noisy nonlinear optimization problems, with and without constraints, under various different assumptions. Apart from Chapter 1 which provides relevant backgrounds, the remaining of thesis is divided into four chapters. In Chapter 2, we establish the theoretical convergence...
At the heart of nonlinear optimization methods lies the solution of linear systems of equations. As the size of the problem increases, it is imperative to use iterative methods, such as the conjugate gradient algorithm, to solve these linear systems. In the context of constrained optimization, it has proved to...