This project is concerned with research in the area of numerical methods for large-scale continuous optimization. The work will focus on iterative algorithms for linear/nonlinear/network programming and complementarity problems. It will cover both the theory (convergence, complexity, etc.) and the practice (implementation, numerical testing, etc.). Methods to be investigated include (i) coordinate descent algorithms, (ii) approximate gradient algorithms, (iii) residual reduction algorithms, (iv) multiplicative multiplier methods, and (v) operator splitting algorithms. Particular attention will be paid to the efficient implementation of these algorithms on sequential and parallel machines. The computer codes produced by the study will be made freely available to the research community for dissemination.
