Intersection theorems on polytopes

Received June 6, 1995 / Revised version received May 26, 1998 Published online October 9, 1998     

Stability in the presence of degeneracy and error estimation

Received February 10, 1997 / Revised version received June 6, 1998 Published online October 9, 1998     

A note on “On Pareto optima, the Fermat-Weber problem, and polyhedral gauges”

Received September 3, 1997 / Revised version received March 20, 1998 Published online October 9, 1998     

Global and polynomial-time convergence of an infeasible-interior-point algorithm using inexact computation

Received April 10, 1996 / Revised version received April 30, 1998 Published online August 18, 1998     

Sample-path solution of stochastic variational inequalities

Received July 30, 1997 / Revised version received June 4, 1998 Published online October 21, 1998     

Analytical properties of the central path at boundary point in linear programming

Received October 15, 1996 / Revised version received January 28, 1998 Published online October 21, 1998     

Search directions in the SDP and the monotone SDLCP: generalization and inexact computation

Received April 15, 1997 / Revised version received July 22, 1998 Published online November 24, 1998     

Partition polytopes over 1-dimensional points

Received March 1996 / Revised version received April 5, 1998 Published online January 20, 1999     

Negative-cycle detection algorithms

Received June 14, 1996 / Revised version received June 22, 1998 Published online January 20, 1999     

A QP-free constrained Newton-type method for variational inequality problems

Received January 5, 1997 / Revised version received November 19, 1997 Published online November 24, 1998     

Fixed–charge continuous knapsack problems and pseudogreedy solutions

Received February 12, 1993 / Revised version received February 6, 1998 Published online February 25, 1999     

Bound constrained quadratic programming via piecewise quadratic functions

1 , the smallest eigenvalue of a symmetric, positive definite matrix, and is solved by Newton iteration with line search. The paper describes the algorithm and its implementation including estimation of λ₁, how to get a good starting point for the iteration, and up- and downdating of Cholesky factorization. Results of extensive testing and comparison with other methods for constrained QP are given. Received May 1, 1997 / Revised version received March 17, 1998 Published online November 24, 1998     

Degeneracy in the multi-source Weber problem

Received June 10, 1996 / Revised version received May 20, 1997 Published online October 21, 1998     

Random Linkage: a family of acceptance/rejection algorithms for global optimisation

Received July 24, 1997 / Revised version received August 9, 1998 Published online January 20, 1999     

Approximating quadratic programming with bound and quadratic constraints

Received May 20, 1997 / Revised version received March 9, 1998 Published online October 9, 1998     

The stable admissions polytope

The stable admissions polytope– the convex hull of the stable assignments of the university admissions problem – is described by a set of linear inequalities. It depends on a new characterization of stability and arguments that exploit and extend a graphical approach that has been fruitful in the analysis of the stable marriage problem. Received: April 10, 1998 / Accepted: June 3, 1999?Published online January 27, 2000     

Infeasible-start primal-dual methods and infeasibility detectors for nonlinear programming problems

ln) iterations, where ν is the parameter of a self-concordant barrier for the cone, ε is a relative accuracy and ρ_f is a feasibility measure. We also discuss the behavior of path-following methods as applied to infeasible problems. We prove that strict infeasibility (primal or dual) can be detected in O(ln) iterations, where ρ_· is a primal or dual infeasibility measure. Received April 25, 1996 / Revised version received March 4, 1998 Published online October 9, 1998     

Continuity properties of the Karush-Kuhn-Tucker point set in quadratic programming problems

Received March 18, 1996 / Revised version received August 8, 1997 Published online November 24, 1998     

Using continuous nonlinear relaxations to solve. constrained maximum-entropy sampling problems

Received January 9, 1997 / Revised version received January 26, 1998 Published online November 24, 1998     

Composition duality and maximal monotonicity

* TL, where T is maximal monotone and L is linear and continuous with adjoint L^*. Received September 9, 1997 / Revised version received June 30, 1998 Published online January 20, 1999