\BOOKMARK [1][]{Outline1}{ Motivation, Notation, Preliminaries}{} \BOOKMARK [2][]{Outline1.1.9}{SDP Duality Gap Example}{Outline1} \BOOKMARK [2][]{Outline1.2.13}{SUBSPACE FORM and MINIMAL REPRESENTATIONS}{Outline1} \BOOKMARK [2][]{Outline1.3.18}{Recession Directions and Minimal Subspaces}{Outline1} \BOOKMARK [1][]{Outline2}{REGULARIZATION for Cone Programs}{} \BOOKMARK [2][]{Outline2.1.24}{Minimal Representations using MINIMAL FACE}{Outline2} \BOOKMARK [2][]{Outline2.2.26}{Minimal Representations using MINIMAL SUBSPACE}{Outline2} \BOOKMARK [2][]{Outline2.3.31}{Constraint Qualifications, CQs, for \(P\)}{Outline2} \BOOKMARK [1][]{Outline3}{Towards a Better regularization}{} \BOOKMARK [2][]{Outline3.1.36}{A Stable Auxiliary Problem}{Outline3} \BOOKMARK [1][]{Outline4}{Numerical Tests}{} \BOOKMARK [1][]{Outline5}{Strict Complementarity and Nonzero Duality Gaps}{} \BOOKMARK [2][]{Outline5.1.49}{Generating Hard SDP Instances}{Outline5} \BOOKMARK [2][]{Outline5.2.54}{Complementarity Partition and Nonzero Duality Gap}{Outline5} \BOOKMARK [1][]{Outline6}{Concluding Remarks}{}