Knowledge Graph (KG)-based Retrieval-Augmented Generation (RAG) shifts the contents of retrieval from narrative text to a relational knowledge network, empowering large language models (LLMs) to harness structured relationships between entities. However, conventional KG-RAG approaches are resource-intensive, requiring either query decomposition with multiple LLM rounds or parameterized static knowledge injection to update the model. Although subgraph reasoning aims to address these issues, most current methods are based on heuristic shortest path and multi-hop graph traversal algorithms. The retrieved subgraphs suffer from incompleteness and semantic drift, and neglect the interaction between subgraph and LLMs in terms of fine-grained structural semantics. We propose a dual-constraint subgraph optimization for KG-RAG (DCTR). It improves subgraph retrieval and generates high-quality subgraphs with structural integrity and information salience for LLMs. Specifically, it formulates subgraph generation as a two-stage graph-theoretic constrained optimization problem to create compact and complete pseudo-labels. Since these pseudo-labels are discrete, a smooth approximation is employed to convert them into a differentiable representation, thereby optimizing the retriever to highlight key information while extracting subgraphs. On two benchmark datasets, DCTR significantly enhances subgraph quality, achieving state-of-the-art performance in LLM reasoning.