A primal affine-scaling algorithm for constrained convex programs

The affine-scaling algorithm was initially developed for linear programming problems. Its extension to problems with a nonlinear objective performs at each iteration a scaling followed by a line search along the steepest descent direction. In this paper we prove that any accumulation point generated by this algorithm when applied to a convex function is an … Read more

The Trust Region Subproblem and Semidefinite Programming

The trust region subproblem (the minimization of a quadratic objective subject to one quadratic constraint and denoted TRS) has many applications in diverse areas, e.g. function minimization, sequential quadratic programming, regularization, ridge regression, and discrete optimization. In particular, it determines the step in trust region algorithms for function minimization. Trust region algorithms are popular for … Read more

Convergence of a Penalty Method for Mathematical Programmingwith ComplementarityConstraints

We adapt the convergence analysis of smoothing (Fukushima and Pang) and regularization (Scholtes) methods to a penalty framework for mathematical programs with complementarity constraints (MPCCs), and show that the penalty framework shares similar convergence properties to these methods. Moreover, we give sufficient conditions for a sequence generated by the penalty framework to be attracted to … Read more

Extension of Quasi-Newton Methods to Mathematical Programs with Complementarity Constraints

Quasi-Newton methods in conjunction with the piecewise sequential quadratic programming are investigated for solving mathematical programming with equilibrium constraints, in particular for problems with complementarity constraints. Local convergence as well as superlinear convergence of these quasi-Newton methods can be established under suitable assumptions. In particular, several well-known quasi-Newton methods such as BFGS and DFP are … Read more

A stable homotopy approach to horizontal linear complementarity problems

We are interested in the solution of Horizontal Linear Complementarity Problems, HLCPs, that is complementarity problems with more variables than equations. Globally metrically regular HLCPs have nonempty solution sets that are stable with respect to “right-hand-side perturbations” of the data, hence are numerically attractive. The main purpose of the paper is to show how the … Read more