Projection algorithms for conic programming with applications in compressed sensing
Master of Arts
Convex conic programming is a general optimization model which includes linear, second-order-cone and semi-definite programming. Many of these programs can be solved via interior-point methods, yet the high demands on memory and computation can make these Newton-based algorithms impractical for large problems. In this thesis, we apply the alternating projection method for convex feasibility problems to some convex conic programming problems. This projection approach does not require solving a linear system of equations at each iteration, but its convergence may be slow. We derive projection formulas for three conic programs, some of which we have not found in the existing literature. These three conic programs arise from recent research on compressed sensing in digital signal processing where a sparse solution, or approximate solution, to an under-determined linear system is sought. We conduct numerical experiments to compare the performance of the projection approach to these three formulations and present numerical results.