Division of Optimization and Systems Theory
Department of Mathematics
The four papers deal with convex quadratic programming, nonconvex nonlinear programming, linear semidefinite programming and linear programming, respectively. The first three have a theoretical flavor, while in the fourth and final paper a number of computational ideas are investigated.
To be more precise, the first paper concerns a boundedness result for sequences of weighted linear least-squares problems related to interior methods for convex quadratic programming. The second one gives a characterization of the behavior of the updates of the multipliers when convergence to infeasible points occur for nonconvex problems. The third paper gives a characterization of the limit point of the central path in linear semidefinite programming, extending previous results to the case where strict complementarity need not hold. The computational experiments in the fourth paper concerns the possibility of using information available through a previous factorization to improve performance of interior methods for linear programming.