Convergence Rate of an Optimization Algorithm for Minimizing Quadratic Functions with Separable Convex Constraints

A new active set algorithm for minimizing quadratic functions with separable convex constraints is proposed by combining the conjugate gradient method with the projected gradient. It generalizes recently developed algorithms of quadratic programming constrained by simple bounds. A linear convergence rate in terms of the Hessian spectral condition number is proven. Numerical experiments, including the frictional three-dimensional (3D) contact problems of linear elasticity, illustrate the computational performance.