In this thesis, we study distributed optimization, where a network of agents, interacting over a directed graph, collaborates to minimize the average of locally-known convex functions. Most of the existing algorithms apply push-sum consensus, which utilizes column-stochastic weight matrices. Column-stochastic weights require each agent to know (at least) its out degree, which may be impractical in e.g., broadcast-based communication protocols. In contrast, we describe FROST (Fast Row-stochastic Optimization with uncoordinated STep-sizes), an optimization algorithm applicable to directed graphs with row-stochastic weights and non-identical step-sizes at the agents. Its implementation is straightforward as each agent locally decides the weights assigned to the incoming information and locally chooses a suitable step-size. Furthermore, we propose a completely linear algorithm which avoids using push-sum (type) techniques and thus leads to less communication and computation over the network of agents. Under the assumptions that each local function is strongly-convex with Lipschitz-continuous gradients, we show that the proposed algorithms linearly converge to the global minimizer with sufficiently small step-sizes. We present numerical simulations to illustrate our theoretical results.