Time series data account for a major part of data supply available today. Time series mining handles several tasks such as classification, clustering, query-by-content, prediction, and others. Performing data mining tasks on raw time series is inefficient as these data are high-dimensional by nature. Instead, time series are first pre-processed using several techniques before different data mining tasks can be performed on them. In general, there are two main approaches to reduce time series dimensionality, the first is what we call landmark methods. These methods are based on finding characteristic features in the target time series. The second is based on data transformations. These methods transform the time series from the original space into a reduced space, where they can be managed more efficiently. The method we present in this paper applies a third approach, as it projects a time series onto a lower-dimensional space by selecting important points in the time series. The novelty of our method is that these points are not chosen according to a geometric criterion, which is subjective in most cases, but through an optimization process. The other important characteristic of our method is that these important points are selected on a dataset-level and not on a single time series-level. The direct advantage of this strategy is that the distance defined on the low-dimensional space lower bounds the original distance applied to raw data. This enables us to apply the popular GEMINI algorithm. The promising results of our experiments on a wide variety of time series datasets, using different optimizers, and applied to the two major data mining tasks, validate our new method.