Given a task in the form of a basic description and its training examples, prompt optimization is the problem of synthesizing the given information into a text prompt for a large language model. Humans solve this problem by also considering the different facets that define a task (e.g., counter-examples, explanations, analogies) and including them in the prompt. However, it is unclear whether existing algorithmic approaches, based on iteratively editing a given prompt or automatically selecting a few in-context examples, can cover the multiple facets required to solve a complex task. In this work, we view prompt optimization as that of learning multiple facets of a task from a set of training examples. We exploit structure in the prompt optimization problem and break down a prompt into loosely coupled semantic sections. The proposed algorithm, UniPrompt, (1) clusters the input space and uses clustered batches so that each batch likely corresponds to a different facet of the task, and (2) utilizes a feedback mechanism to propose adding, editing or deleting a section, which in turn is aggregated over a batch to capture generalizable facets. Empirical evaluation on multiple datasets and a real-world task shows that prompts generated using UniPrompt obtain higher accuracy than human-tuned prompts and those from state-of-the-art methods. In particular, our algorithm can generate long, complex prompts that existing methods are unable to generate.