Anita Varga – Optimization Online

Dual certificates of primal cone membership

Published: 2025/06/14, Updated: 2026/03/25

Cone Programming, Convex Optimization, Semi-definite Programming Cone membership certificates, duality, Interior point algorithms, Nonsymmetric conic optimization, polynomial optimization, self-concordant barrier functions

We discuss optimization problems over convex cones in which membership is difficult to verify directly. In the standard theory of duality, vectors in the dual cone \(K^*\) are associated with separating hyperplanes and interpreted as certificates of non-membership in the primal cone \(K\). Complementing this perspective, we develop easily verifiable certificates of membership in \(K\) … Read more

Interior-point algorithms with full Newton steps for nonsymmetric convex conic optimization

Published: 2025/02/21

Dávid Papp

Anita Varga

Cone Programming, Convex Optimization feasible method, Interior point algorithms, Nonsymmetric conic optimization, polynomial complexity

We design and analyze primal-dual, feasible interior-point algorithms (IPAs) employing full Newton steps to solve convex optimization problems in standard conic form. Unlike most nonsymmetric cone programming methods, the algorithms presented in this paper require only a logarithmically homogeneous self-concordant barrier (LHSCB) of the primal cone, but compute feasible and \(\varepsilon\)-optimal solutions to both the … Read more