Abstract: In this manuscript, we discuss the problem of determining the optimum stratification of a study (or main) variable based on the auxiliary variable that follows a uniform distribution. If the stratification of survey variable is made using the auxiliary variable it may lead to substantial gains in precision of the estimates. This problem is formulated as a Nonlinear Programming Problem (NLPP), which turn out to multistage decision problem and is solved using dynamic programming technique.
Abstract: In this paper, we propose a multiple objective optimization model with respect to portfolio selection problem for investors looking forward to diversify their equity investments in a number of equity markets. Based on Markowitz-s M-V model we developed a Fuzzy Mixed Integer Multi-Objective Nonlinear Programming Problem (FMIMONLP) to maximize the investors- future gains on equity markets, reach the optimal proportion of the budget to be invested in different equities. A numerical example with a comprehensive analysis on artificial data from several equity markets is presented in order to illustrate the proposed model and its solution method. The model performed well compared with the deterministic version of the model.
Abstract: In this paper, a nonlinear model predictive swing-up
and stabilizing sliding controller is proposed for an inverted
pendulum-cart system. In the swing up phase, the nonlinear model
predictive control is formulated as a nonlinear programming problem
with energy based objective function. By solving this problem at
each sampling instant, a sequence of control inputs that optimize the
nonlinear objective function subject to various constraints over a
finite horizon are obtained. Then, this control drives the pendulum to
a predefined neighborhood of the upper equilibrium point, at where
sliding mode based model predictive control is used to stabilize the
systems with the specified constraints. It is shown by the simulations
that, due to the way of formulating the problem, short horizon
lengths are sufficient for attaining the swing up goal.