In　the　universal　facility　location　problem,　we　are　given　a　set　of　clients　and　facilities.　Our　goal　is　to　find　an　assignment　such　that　the　total　connection　and　facility　cost　is　minimized.　The　connection　cost　is　proportional　to　the　distance　between　each　client　and　its　assigned　facility,　whereas　the　facility　cost　is　a　nondecreasing　function　with　respect　to　the　total　number　of　clients　assigned　to　the　facility.　The　universal　facility　location　problem　generalizes　several　classical　facility　location　problems,　including　the　uncapacitated　facility　location　problem　and　the　capacitated　facility　location　problem　(both　hard　and　soft　capacities).　This　work　considers　the　universal　facility　location　problem　with　linear　penalties,　where　each　client　can　be　rejected　for　service　with　a　penalty.　The　objective　is　to　minimize　the　total　connection,　facility　and　penalty　cost.　We　present　a　(5.83　+　epsilon)-approximation　local　search　algorithm　for　this　problem.