This　paper　demonstrates　that　2D　pose　SLAM　has　an　underlining　near　convex　structure　when　formulated　as　a　least　squares　(LS)　optimization　problem.　By　introducing　new　variables　and　some　approximations,　the　LS　pose　SLAM　problem　can　be　formulated　as　a　quadratically　constrained　quadratic　programming　(QCQP)　problem.　The　QCQP　formulation　can　then　be　relaxed　into　a　semi-definite　programming　(SDP)　problem　which　is　convex.　Unique　solution　to　the　convex　SDP　problem　can　be　obtained　without　initial　state　estimate　and　can　be　used　to　construct　a　candidate　solution　to　the　original　LS　pose　SLAM　problem.　Simulation　datasets　and　the　Intel　Research　Lab　dataset　have　been　used　to　demonstrate　that　when　the　relative　pose　information　contain　noises　with　reasonable　level,　the　candidate　solution　obtained　through　the　relaxation　is　very　close　to　the　optimal　solution　to　the　LS　SLAM　problem.　Thus　in　practice,　the　candidate　solution　can　serve　as　either　an　approximate　solution　or　a　good　initial　guess　for　a　local　optimization　algorithm　to　obtain　the　optimal　solution　to　the　LS　pose　SLAM　problem.