Sensitivity Analysis For The Second-Order Cone Programs

This thesis mainly considers the sensitivity of central solutions in second-order cone programs and sensitivity result of strictly complementary stationary point in nonlinear second-order cone programs. It consists of three chapters.Chapter 1 gives an introduction of the thesis, which mainly discusses the current development of the discussed issues, i.e. second-order cone programs, the main contribution of this paper is also listed in this chapter.In Chapter 2, we consider the properties of the analytic central path of a second-order cone programming problem under perturbation of the right hand side of the constraints, including the limiting behavior when the central optimal solution is approached. Under primal-dual Slater condition and strict comple-mentarity assumption, we show that on the central path any directional deriva-tive with respect to the right hand side of the constraints is bounded, and even converges as the central optimal solution is approached.In Chapter 3, we consider the sensitivity of the locally unique and strictly complementary stationary point of a nonlinear second-order cone programming problem under perturbation of the date. Under Slater condition and strict com-plementarity assumption, we establish that the solution of the perturbation prob-lem is a function of perturbation, and its derivatives can be given via a solution of a linear equation system.