Sharif Digital Repository

Column generation technique has became a very important tool in the solution of linear programming problems. Column generation techniques start with solving a reduced version of the master problem. Recently, variations of the standard column generation approach have been proposed which use interior point of the dual feasible set instead of optimal slutions. So, primal-dual column generation technique uses a primal-dual interior point method to obtain well-centered non-optimal solutions of the restricted master problem. We show that the method converges to an optimal solution of the master problem. Then, an improved primal simplex algorithm (IPS) for degenerate linear problems is proposed.... 

Discovery of the effect of a massive object on the light path, reaching its exact formalism through general relativity and utilizing this phenomenon as a natural lens, opened a new window in astronomical research. Gravitational lensing occurs in three different ways; strong lensing, weak lensing, and microlensing which we focus on the third one. Gravitational microlensing is useful in studying dark matter candidates, discovering exoplanets, finding the surface properties of stars, and calculating the mass distribution of galactic objects. From a typical microlensing event, Einstein crossing time is obtained which is the time scale of source star passing by the lens. This is the only...