Generating and Measuring Instances of Hard Semidefinite Programs, SDP

Linear Programming, LP, problems with finite optimal value have a zero duality gap and a primal-dual strictly complementary optimal solution pair. On the other hand, there exists Semidefinite Programming, SDP, problems which have a nonzero duality gap (different primal and dual optimal values; not both infinite). The duality gap is assured to be zero if … Read more

A Stable Iterative Method for Linear Programming

This paper studies a new primal-dual interior/exterior-point method for linear programming. We begin with the usual perturbed primal-dual optimality equations $F_\mu(x,y,z)=0$. Under nondegeneracy assumptions, this nonlinear system is well-posed, i.e. it has a nonsingular Jacobian at optimality and is not necessarily ill-conditioned as the iterates approach optimality. We use a simple preprocessing step to eliminate … Read more