An explicit solution for a multimarginal mass transportation problem

We construct an explicit solution for the multimarginal transportation problem on the unit cube $[0,1]^3$ with the cost function $xyz$ and one-dimensional uniform projections. We show that the primal problem is concentrated on a set with non-constant local dimension and admits many solutions, whereas the solution to the corresponding dual problem is unique (up to addition of constants).Comment: 31 pages, 4 figures. The paper was completely rewritten. Heuristic considerations to find a solution of the primal problem added. Algorithm to find the primal problem solution numerically added (arbitrary marginals). The construction was generalized for a C(ln x + ln y + ln z), C is convex. Measure on the triangle was found with the support singular with respect to the Lebesgue measur

On Some Optimal Control Problems Arising from Project Management

The complexity of modern industrial and governmental enterprises with the consequent increase in the quantity and sophistication of managerial decisions, on the one hand, and the fact that the payoffs from good decisions are greater than ever before, on the other hand, offer a challenge to build up conforming scientific methods for decision making. The systems programmed approach or the programmed control method is a practical method to manage large and complex systems. In general it is a feed-back decision-making process which implies many time planning processes and consists of such elements as forecasting, formulation of goals and objectives, collection of available alternative strategies to achieve the goals, selection of the best alternative, realization of the strategy, comparison of the results with predicted outcome, new forecasting, reformulation of goals and so on. Thus the process includes both formal (strict) and informal (heuristic) procedures. To find the application and to emphasize the necessity for using rigorous mathematical methods in the decision-making process in the economic systems, we shall briefly describe some decision-making elements and the corresponding mathematical models

Open-Category Classification by Adversarial Sample Generation

In real-world classification tasks, it is difficult to collect training samples from all possible categories of the environment. Therefore, when an instance of an unseen class appears in the prediction stage, a robust classifier should be able to tell that it is from an unseen class, instead of classifying it to be any known category. In this paper, adopting the idea of adversarial learning, we propose the ASG framework for open-category classification. ASG generates positive and negative samples of seen categories in the unsupervised manner via an adversarial learning strategy. With the generated samples, ASG then learns to tell seen from unseen in the supervised manner. Experiments performed on several datasets show the effectiveness of ASG.Comment: Published in IJCAI 201