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First, it regularizes the objective function by adding a quadratic term which depends on primal-dual solution of the previous iterate. ... Let us explore an immediate consequence of Condition 2. ... A.1 Properties of self-concordant function Let us first recall the definition of a self concordant function. holds for any x ∈ C and h ∈ R m . ...doi:10.13097/archive-ouverte/unige:396 fatcat:vnqo3djbjfbvlbtops6wbe54qq