# Solving nearly-separable quadratic optimization problems as nonsmooth equations

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## Abstract

An algorithm for solving nearly-separable quadratic optimization problems (QPs) is presented. The approach is based on applying a semismooth Newton method to solve the implicit complementarity problem arising as the first-order stationarity conditions of such a QP. An important feature of the approach is that, as in dual decomposition methods, separability of the dual function of the QP can be exploited in the search direction computation. Global convergence of the method is promoted by enforcing decrease in component(s) of a Fischer–Burmeister formulation of the complementarity conditions, either via a merit function or through a filter mechanism. The results of numerical experiments when solving convex and nonconvex instances are provided to illustrate the efficacy of the method.

### Keywords

Quadratic optimization problems Dual decomposition Complementarity problems Semismooth Newton methods Fischer–Burmeister function### Mathematics Subject Classification

49M05 49M15 49M27 49M29 65K05 65K10 90C20 90C33### References

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