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Using a robust optimization approach, we first establish necessary and sufficient optimality conditions for weakly efficiencies of the corresponding robust multiobjective optimization problem. These optimality criteria are expressed in terms of sums-of-squares conditions and linear matrix inequalities, which provide a numerically checkable certificate of the solvability of the given optimality conditions. We then propose a dual multiobjective problem by means of sums-of-squares and linear matrix inequalities to the robust multiobjective SOS-convex polynomial optimization problem and examine weak, strong, and converse duality relations between them. In addition, we consider a semidefinite linear programming (SDP) weighted-sum relaxation problem for verifying weighted-sum efficient values of the primal problem.<\/jats:p>","DOI":"10.1137\/17m1143484","type":"journal-article","created":{"date-parts":[[2018,9,11]],"date-time":"2018-09-11T16:35:27Z","timestamp":1536683727000},"page":"2466-2488","source":"Crossref","is-referenced-by-count":31,"title":["Linear Matrix Inequality  Conditions and Duality for a Class of Robust Multiobjective  Convex Polynomial Programs"],"prefix":"10.1137","volume":"28","author":[{"given":"Thai Doan","family":"Chuong","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,9,11]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/110856010"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"G. Blekherman, P. A. Parrilo, and R. Thomas, eds.\n                      Semidefinite Optimization and Convex Algebraic Geometry\n                      , MOS-SIAM Ser. Optim. 13, MOS, SIAM, Philadelphia, 2013,https:\/\/doi.org\/10.1137\/1.9781611972290.","DOI":"10.1137\/1.9781611972290"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"A. Ben-Tal, L. El Ghaoui, and A. Nemirovski,\n                      Robust Optimization\n                      , Princeton Ser. Appl. 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