Optimization　problems　on　unknown　low-dimensional　structures　given　by　high-dimensional　data　belong　to　the　field　of　optimizations　on　manifolds.　Though　recent　developments　have　advanced　the　theory　of　optimizations　on　manifolds　considerably,　when　the　unknown　low-dimensional　manifold　is　given　in　the　form　of　a　set　of　data　in　a　high-dimensional　space,　a　practical　optimization　method　has　yet　to　be　developed.　Here,　we　propose　a　neural　network　approach　to　these　optimization　problems.　A　neural　network　is　used　to　approximate　a　neighborhood　of　a　point,　which　will　turn　the　computation　of　a　next　point　in　the　searching　process　into　a　local　constraint　optimization　problem.　Our　method　ensures　the　convergence　of　the　process.　The　proposed　approach　applies　to　optimizations　on　manifolds　embedded　into　Euclidean　spaces.　Experimental　results　show　that　this　approach　can　effectively　solve　optimization　problems　on　unknown　manifolds.　The　proposed　method　provides　a　useful　tool　to　the　field　of　study　low-dimensional　structures　given　by　high-dimensional　data.