Semidefinite and Second Order Cone Programming Seminar Fall 2012 Project: Robust Optimization and its Application of Robust Portfolio Optimization

There are several different methods to treat uncertainty in literacy. First, sensitivity analysis which is a post-optimization method analyzing stability of generated solutions. Second, stochastic programming is a modeling approach, and this method is limited to that the uncertainty is stochastic in nature. Third, “Robust Mathematical Programming” is that a candidate solutions allowing to violate the “scenario realizations” of the constraints instead of considering fixed “nominal” data for several scenarios considered, and add penalty terms in the objective function. [2] The robust optimization is a method to handle deterministic uncertainty in optimization problems [4]. Majority of uncertain data are due to prediction errors, measurement errors, and implementation errors. Moreover, small errors in data values can make optimal solutions highly infeasible, and the robust optimization prevent the infeasible solutions. This paper first summarizes the basic concept of robust optimization [1] and shows its application of robust portfolio optimization.