Logic-Based Outer Approximation for the Design of Discrete-Continuous Dynamic Systems with Implicit Discontinuities

We address the optimization of discrete-continuous dynamic optimization problems using a disjunctive multistage modeling framework, with implicit discontinuities, which increases the problem complexity since the number of continuous phases and discrete events is not known a-priori. After setting a fixed alternative sequence of modes, we convert the infinite-dimensional continuous mixed-logic dynamic (MLDO) problem into a finite dimensional discretized GDP problem by orthogonal collocation on finite elements. We use the Logic-based Outer Approximation algorithm to fully exploit the structure of the GDP representation of the problem. This modelling framework is illustrated with an optimization problem with implicit discontinuities (diver problem).

Missing mixed mode: elemental structures

One of the main concerns is the nature of the missing values. Let’s consider extremes for simplicity. If missing at random we have not to care about. But if missing shows structures that covariate with substantive variables we have to make decisions. There are, in fact, several options to take. We are speaking about one country, one mode. But if you go cross-cultural (or more precisely, cross-state nations) and mixed modes many questions raise. For example, the simple one. What are we comparing? Reports and books usually go straight into variables distributions and coefficient comparisons. This is possible because the annalist presume "tabula rasa" effect from data collections procedures. But this is not, frequently, the real situation. This paper will expose the mixed missing mode imprint in international surveys. This will help to evaluate how deal with this problem. Also, to consider the real meaning of observed cross-national differences.