Distributed constraint optimization (DCOP) has proven to be a promising approach to address coordination, scheduling and task allocation in largescale multiagent networks, in domains involving sensor networks, teams of unmanned air vehicles, or teams of software personal assistants and others. Locally optimal approaches to DCOP suggest themselves as appropriate for such large-scale multiagent networks, particularly when such networks are accompanied by lack of high-bandwidth communications among agents. K-optimal algorithms provide an important class of these locally optimal algorithms, given analytical results proving quality guarantees. Previous work on koptimality, including its theoretical guarantees, focused exclusively on soft constraints. This paper extends the results to DCOPs with hard constraints. It focuses in particular on DCOPs where such hard constraints are resource constraints which individual agents must not violate. We provide two key results in the context of such DCOPs. First we provide reward-independent lower bounds on the quality of k-optima in the presence of hard (resource) constraints. Second, we present algorithms for k-optimality given hard resource constraints, and present detailed experimental results over DCOP graphs of 1000 agents with varying constraint density.