Advances in convex optimization: Conic programming

Abstract. During the last two decades, major developments in convex optimization were focus-ing on conic programming, primarily, on linear, conic quadratic and semidefinite optimization. Conic programming allows to reveal rich structure which usually is possessed by a convex pro-gram and to exploit this structure in order to process the program efficiently. In the paper, we overview the major components of the resulting theory (conic duality and primal-dual interior point polynomial time algorithms), outline the extremely rich “expressive abilities ” of conic quadratic and semidefinite programming and discuss a number of instructive applications