Now showing items 1-6 of 6
Effective computation of the analytic center of the solution set in linear programming using primal-dual interior-point methods
The centrality property satisfied by the analytic center of the solution set makes its computation very valuable for some linear programming applications. One such application coming from the economic and management sciences ...
A robust choice of the Lagrange multipliers in the successive quadratic programming method
We study the choice of the Lagrange multipliers in the successive quadratic programming method (SQP) applied to the equality constrained optimization problem. It is known that the augmented Lagrangian SQP-Newton method ...
Structured secant updates for nonlinear constrained optimization
Two new updates are presented, the UHU update and a modified Gurwitz update, for approximating the Hessian of the Lagrangian in nonlinear constrained optimization problems. Under the standard assumptions, the new UHU ...
Convergence properties of the Barzilai and Borwein gradient method
In a recent paper, Barzilai and Borwein presented a new choice of steplength for the gradient method. Their choice does not guarantee descent in the objective function and greatly speeds up the convergence of the method. ...
Effective finite termination procedures in interior-point methods for linear programming
Due to the structure of the solution set, an exact solution to a linear program cannot be computed by an interior-point algorithm without adding features, such as finite termination procedures, to the algorithm. Finite ...
A new class of preconditioners for large-scale linear systems from interior-point methods for linear programming
A new class of preconditioners for the iterative solution of the linear systems arising from interior point methods is proposed. For many of these methods, the linear systems come from applying Newton's method on the ...