This　article　designs　an　optimal　observer-based　output　feedback　control　for　traffic　breakdown　to　dissolve　traffic　congestion　using　the　backstepping　method　and　optimization.　The　linearized　Aw-Rascle-Zhang　model　is　used　to　represent　the　congested　traffic　dynamics　resulting　from　traffic　breakdown.　Based　on　the　factors　leading　to　traffic　breakdown,　we　take　into　account　the　boundary　conditions　consisting　of　a　boundary　with　a　constant　density　and　a　speed　drop　at　the　upstream　inlet　of　a　bottleneck,　and　a　boundary　with　a　disturbance　of　inflow　(high　traffic　demand)　at　the　inlet　of　the　road　segment　under　consideration.　To　dissolve　traffic　congestion,　a　dynamic　feedback　controller　is　designed　at　the　upstream　boundary.　By　using　the　backstepping　approach,　an　observer-based　output　feedback　controller　is　computed　to　guarantee　the　integral　input-to-state　stability　of　the　closed-loop　system.　By　establishing　an　optimization　problem　and　solving　it,　the　optimal　value　of　the　considered　class　controller　is　obtained.　The　performance　of　the　output　feedback　controller　is　also　validated　by　numerical　simulations.