This thesis develops complementary perspectives on optimization, combining theoretical advances in nonsmooth nonconvex algorithms and applied models for decision-making under uncertainty, emphasizing both rigor and applicability. In nonsmooth nonconvex optimization, stochastic gradient methods are widely used but lack finite-time complexity guarantees. A major breakthrough occurred in 2020 with the introduction of the INGD algorithm, which established the first such guarantees for minimizing general locally Lipschitz functions. Building on this result, the first part of this thesis makes two contributions. First, it proposes the first deterministic algorithm for nonsmooth nonconvex optimization with finite-time complexity guarantees, achieving the optimal complexity bound. Second, it develops a step-size adaptation framework that accelerates convergence from sublinear to nearly linear rates, providing new theoretical insights into the design of efficient algorithms for nonsmooth nonconvex problems. A second line of work applies optimization-based modeling to epidemiology under data uncertainty. While ex-post sensitivity analysis assesses uncertainty after model construction and ex-ante stochastic programming relies on known probability distributions that are often unavailable, this thesis adopts robust optimization as an alternative ex-ante framework. The resulting models produce reliable decisions under uncertainty without requiring distributional assumptions.