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Strong Lagrangian Duality via Quasi-Relative Interior for Constrained Support Vector Machines

A constraint-qualification result establishing strong Lagrangian duality for nonsmooth convex optimization in Hilbert spaces using the quasi-relative interior, together with its application to a generalized support vector machine that adds a geometric constraint or regularizer on the separating hyperplane, analyzed by Lagrangian duality and solved with a subgradient and a primal-dual algorithm.

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Lagrange Multipliers and Duality with Applications to Constrained Support Vector Machine Nguyen Mau

Uses the quasi-relative interior (a generalization of the relative interior for convex sets in infinite-dimensional spaces) to weaken the constraint-qualification needed for strong Lagrangian duality…