Abstract
This paper considers implementable versions of a conceptual convex optimization algorithm which provides a high-speed (super-linear, quadratic and finite) convergence for broad classes of convex optimization problems. The algorithm can be best viewed in the space of conjugate variables and as such it implicitly solves optimality conditions by sequential projection on the epigraph of conjugate function. The implementable version of this algorithm tries to solve projection problems approximately by construction of the inner approximations of the epigraph up to sufficient accuracy.
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