Optimization Models for Applications in Portfolio Management and Advertising Industry

Optimization problems in two different application fields are investigated: the first one is the popular portfolio optimization problem and the second one is the newly developed online display advertising problem. The portfolio optimization problem has two main concerns: an appropriate statistical input data, which is improved with the use of factor model and, the inclusion of the transaction cost function into the original objective function. Two methods are applied to solve the optimization problem, namely,the conditional value at risk (CVaR) method and the reliability based (RB) method. Asset allocation problem in finance continues to be of practical interest because decisions as to where to invest must be made to maximize the total return and minimizing the risk of not attaining the target return. However, the commonly used Markowitz method, also known as the mean-variance approach, uses historic stock prices data and has been facing problems of parameter estimation and short sample errors. An alternative method that attempts to overcome this problem is the use of factor models. This thesis will explain this model in addition to explaining the basic portfolio optimization problem. Conditional value at risk and the reliability based optimization method are applied to solve the portfolio optimization problem with the consideration of transaction costs in the objective function.They are applied and evaluated by simulation in terms of their convergence, efficiency and results. The online display advertising problem extends a normal deterministic revenue optimization model to a stochastic allocation model. The incorporation of randomness makes it more realistic for the estimation of demand, supply and market price. Revenues are considered as a combination of gains from guaranteed contracts and unguaranteed spot market. The objective is not only to maximize the revenue but also to consider the quality of ads, so that the whole market obtains long-term benefits and stability. The thesis accomplishes in solving the online display advertising allocation problem in a stochastic case with the measure of conditional value at risk algorithm

Novel MEMS Tunable Capacitors with Linear Capacitance-Voltage Response Considering Fabrication Uncertainties

Electrostatically actuated parallel-plate MEMS tunable capacitors are desired elements for different applications including sensing, actuating and communications and RF (radio frequency) engineering for their superior characteristics such as quick response, high Q-factor and small size. However, due to the nature of their coupled electrostatic-structural physics, they suffer from low tuning range of 50% and have nonlinear capacitance-voltage (C-V) responses which are very sensitive to the voltage change near pull-in voltage. Numerous studies in the literature introduce new designs with high tunability ranging from 100% to over 1500%, but improvement of the nonlinearity and high sensitivity of the capacitor response have not received enough attention. In this thesis, novel highly tunable capacitors with high linearity are proposed to reduce sensitivity to the voltage changes near pull-in. The characteristic equations of a perfectly linear capacitor are first derived for two- and three-plate capacitors to obtain insight for developing linear capacitance-voltage responses. The devices proposed in this research may be classified into three categories: designs with nonlinear structural rigidities, geometric modifications and flexible moving electrodes. The concept of nonlinear supporting beams is exploited to develop parallel-plate capacitors with partially linear C-V curves. Novel electrodes with triangular, trapezoidal, butterfly, zigzag and fishbone shapes and structural/geometric nonlinearities are used to increase the linearity and tuning ratio of the response. To investigate the capacitors' behavior, an analytical approximate model is developed which can drastically decrease the computation time. The model is ideal for early design and optimization stages. Using this model, design variables are optimized for maximum linearity of the C-V responses. The results of the proposed modeling approach are verified by ANSYS FEM simulations and/or experimental data. When the fabrication process has dimensional limitations, design modifications and geometric enhancements are implemented to improve the linearity of the C-V response. The design techniques proposed in this thesis can provide tunabilities ranging from 80% to over 350% with highly linear regions in resulting C-V curves. Due to the low sensitivity of the capacitance to voltage changes in new designs, the entire tuning range is usable. Furthermore, the effect of fabrication uncertainties on parallel-plate capacitors performance is studied and a sensitivity analysis is performed to find the design variables with maximum impact on the C-V curves. An optimization method is then introduced to immunize the design against fabrication uncertainties and to maximize the production yield for MEMS tunable capacitors. The method approximates the feasible region and the probability distribution functions of the design variables to directly maximize the yield. Numerical examples with two different sets of design variables demonstrate significant increase in the yield. The presented optimization method can be advantageously utilized in design stage to improve the yield without increasing the fabrication cost or complexity