With　robot-controlled　linac　positioning,　robotic　radiotherapy　systems　such　as　CyberKnife　significantly　increase　freedom　of　radiation　beam　placement,　but　also　impose　more　challenges　on　treatment　plan　optimization.　The　resampling　mechanism　in　the　vendor-supplied　treatment　planning　system　(MultiPlan)　cannot　fully　explore　the　increased　beam　direction　search　space.　Besides,　a　sparse　treatment　plan　(using　fewer　beams)　is　desired　to　improve　treatment　efficiency.　This　study　proposes　a　singular　value　decomposition　linear　programming　(SVDLP)　optimization　technique　for　circular　collimator　based　robotic　radiotherapy.　The　SVDLP　approach　initializes　the　input　beams　by　simulating　the　process　of　covering　the　entire　target　volume　with　equivalent　beam　tapers.　The　requirements　on　dosimetry　distribution　are　modeled　as　hard　and　soft　constraints,　and　the　sparsity　of　the　treatment　plan　is　achieved　by　compressive　sensing.　The　proposed　linear　programming　(LP)　model　optimizes　beam　weights　by　minimizing　the　deviation　of　soft　constraints　subject　to　hard　constraints,　with　a　constraint　on　the　l(1)　norm　of　the　beam　weight.　A　singular　value　decomposition　(SVD)　based　acceleration　technique　was　developed　for　the　LP　model.　Based　on　the　degeneracy　of　the　influence　matrix,　the　model　is　first　compressed　into　lower　dimension　for　optimization,　and　then　back-projected　to　reconstruct　the　beam　weight.　After　beam　weight　optimization,　the　number　of　beams　is　reduced　by　removing　the　beams　with　low　weight,　and　optimizing　the　weights　of　the　remaining　beams　using　the　same　model.　This　beam　reduction　technique　is　further　validated　by　a　mixed　integer　programming　(MIP)　model.　The　SVDLP　approach　was　tested　on　a　lung　case.　The　results　demonstrate　that　the　SVD　acceleration　technique　speeds　up　the　optimization　by　a　factor　of　4.8.　Furthermore,　the　beam　reduction　achieves　a　similar　plan　quality　to　the　globally　optimal　plan　obtained　by　the　MIP　model,　but　is　one　to　two　orders　of　magnitude　faster.　Furthermore,　the　SVDLP　approach　is　tested　and　compared　with　MultiPlan　on　three　clinical　cases　of　varying　complexities.　In　general,　the　plans　generated　by　the　SVDLP　achieve　steeper　dose　gradient,　better　conformity　and　less　damage　to　normal　tissues.　In　conclusion,　the　SVDLP　approach　effectively　improves　the　quality　of　treatment　plan　due　to　the　use　of　the　complete　beam　search　space.　This　challenging　optimization　problem　with　the　complete　beam　search　space　is　effectively　handled　by　the　proposed　SVD　acceleration.