Strong Duality and Minimal Representations for Cone Optimization


The elegant results for strong duality and strict complementarity for 
LP can fail for cone programming over nonpolyhedral cones.  
We take a fresh look at known and new results for duality, optimality, 
constraint qualifications, and strict complementarity.  These results 
include: weakest and universal CQs; duality and characterizations of 
optimality that hold without any CQ; geometry of nice and devious cones; 
the geometric relationships between zero duality gaps, strict complementarity,
and the facial structure of cones; and, the connection between theory 
and empirical evidence for lack of a CQ and failure of strict complementarity.