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...A second order smooth variational principle on riemannian manifolds daniel azagra and robb fry abstract we establish valid for functions dened possibly innite dimensional which are uniformly locally convex have strictly positive injectivity ra dius bounded sectional curvature introduction main result it is well known that continuous function an manifold or banach space does not generally attain minimum in situations there would typically exist minimizers if the were nite instance when inmum of interior ball smaller than boundary fact as shown with no critical points dense every hilbert this may be viewed strong approximate version morse sard theorem so given should expect to able nd any point whatever overall shape might none quite inconvenient because many important problems pdes optimization admit equivalent formulations minimization prob lems one dierentiable lower semi etc functional usually asked minimizer will provide solution initial problem under several classes rather re stric...