This paper proposes a novel geometric optimization framework that deeply integrates the cone geometry in convex cone programming with the intrinsic differential structure in manifold optimization, constructing a new geometric object—the cone-manifold structure (M, K_x). In this structure, the convex cone is no longer considered as an external feasible region but is embedded in the tangent space of the manifold, forming a position-dependent directional geometric constraint. Based on this, we establish a novel continuous-time optimization system—the cone-manifold intrinsically coupled variational flow—and prove that: (1) The equilibrium point is strictly equivalent to the generalized KKT conditions; (2) The system has a unique solution on a complete Riemannian manifold; (3) The system has a strictly dissipative geometric structure; (4) Classical cone programming and Riemannian optimization are both degenerate cases of it. This theory achieves the unification of convex geometry, dual cone structure, and manifold differential structure, providing a new theoretical framework for high-dimensional structured optimization, matrix manifold optimization, and nonlinear constraint problems..