| This work conveys various results regarding condition numbers for linear programming. Like traditional condition numbers for linear equations, these numbers aim to capture how changes in the data of the linear program affect properties of the solutions.;For a feasible conic system of constraints;This thesis addresses three main themes. First, we study some geometric properties of the set of infeasible perturbations of a conic system. It is shown how the geometry of infeasible perturbations for linear equations extends naturally to conic systems.;Second, we propose a way to solve the problem of finding a solution for a conic system of constraints by reformulating the problem as an optimization problem to be solved via interior-point methods (IPMs). The approach provides both backward and forward-approximate solutions for a given conic system. The behavior of the IPM bears a close connection with the condition number of the conic system; in particular, the condition numbers of the linear systems that need to be solved when applying the IPM are always bounded in terms of the condition number of the conic system.;Third, we combine some key results established in Chapters 2 and 3 to design several schemes to effectively estimate the condition number of a conic system. In addition to theoretical guarantees on the quality of the estimates, we perform numerical experiments to illustrate the behavior of the proposed schemes in practice. |
