Risk-Averse Stochastic Programming: Time Consistency and Optimal Stopping

This paper addresses time consistency of risk-averse optimal stopping in stochastic optimization. It is demonstrated that time-consistent optimal stopping entails a specific structure of the functionals describing the transition between consecutive stages. The stopping risk measures capture this structural behavior and allow natural dynamic equations for risk-averse decision making over time. Consequently, associated optimal policies satisfy Bellman’s principle of optimality, which characterizes optimal policies for optimization by stating that a decision maker should not reconsider previous decisions retrospectively. We also discuss numerical approaches to solving such problems.

Malliavin calculus used to derive a stochastic maximum principle for system driven by fractional Brownian and standard Wiener motions with application

We consider a stochastic control problem in the case where the set of the control domain is convex, and the system is governed by fractional Brownian motion with Hurst parameter {H\in(\frac{1}{2},1)} and standard Wiener motion. The criterion to be minimized is in the general form, with initial cost. We derive a stochastic maximum principle of optimality by using two famous approaches. The first one is the Doss–Sussmann transformation and the second one is the Malliavin derivative.

Physico-theoretical basis of the mesoscopic approach to the study of soil and climatic regulations

Aim of the study. The aim of the work was to review critically the practice of applying system approach in soil research and identify existing problems; to consider the cognitive potential of micro- and macroscopic approaches in computational simulation of soil-bioclimatic regularities. Methodology. Mathematical simulation. Results of the study. A new mesoscopic approach to the study of the structure of soil-bioclimatic areas is proposed. It is based on two principles referred to as the principle of invariance and the principle of optimality. Application of these principles makes it possible to express the regularities in soil-climate relationship in the form of a single universal quantitative dependence. The study showed that a mathematical model built on the basis of these principles resulted in the emergence of new generalized concepts, logically combining the previously considered to be unrelated concepts of hydro- and thermal series introduced by V.R. Volobuev, the Vysotsky - Ivanov moisture coefficient and the radiation dryness index by M. Budyko. In addition, the simulation showed that the concepts elucidating the indicator of the radiation energy utilization by biogeocenosis were represented by the interrelated coefficients of the heat and precipitation utilization in soils. The coefficients were also shown to have specific values ​​for different soil-bioclimatic areas. On the basis of the new indicators, soils were grouped in such a way as to produce patterns essentially different in many details from the conventional grouping. Conclusions. The new concepts represent a unified integral system, and the approach as a whole can be considered as an alternative physico-theoretical way to describe natural laws and regularities by using extreme (variational) methodology.

SISTEM INFORMASI GEOGRAFIS PENENTUAN RUTE TERPENDEK LOKASI VILLA MENGGUNAKAN ALGORITMA FLOYD WARSHALL

District Tawangmangu has many types of villa that can be able to the local people and the community itself. Information about where the villa is needed by tourists also the general public is the route information to the villa in district Tawangmangu. The aim of the research is to apply Floyd Warshall algorithm in finding the shortest route for villa in Tawangmangu District which has 150 and about 30 which will be displayed in the Web interface with the help of Google Maps API. The closest villa location to the Grojokan sewu tourist is the villa Indra Sari with a yield of 245 meters. As well as comparisons with Google Maps got results 80% of the 30 different test paths and due diligence with respondents showed a feasibility rate of 88,75% indicating that the application made is well-deserved by the user, Floyd Warshall algorithm is applied because the principle held by the algorithm Floyd Warshall is the principle of optimality. The result is an application that can show the shortest route, along with from the starting location to the destination location of the villa.

The common problem of vectorial optimization in the technological safety management

In the work examined: possibility of the use of vectorial optimization at a management technogenic safety; some problem aspects of such use; general issue of vectorial optimization at a management technogenic safety and mathematical formalization of this problem comes true.The marked is caused: by complication and importance of practical problems at military to business, for the decision of that the vehicle of analysis of operations is attracted; by inaccuracy of traditional methods of scalar (onecriterion) optimization at the decision of similar problems; by possibilities of vectorial, multicriterion approach in relation to a search and optimization of administrative decisions at consideration of difficult processes and systems of any nature, including, management technogenic safety.It is set that basic difficulties of decision of vectorial tasks to optimization of decisions in relation to a management technogenic safety are related to the specification of the initial formalized model, with transformation of her to the kind, comfortable for a choice optimal decision. Thus there is a necessity for the decision of three fundamental problems on that the rightness of optimal choice depends in a great deal: choice of principle of optimality; choice of principle of normalization; choice of principle of taking into account of priority.Research results can be drawn on during organization of liquidation of consequences of emergencies of different character and realization of management technogenic safety in the aspect of search of optimal decision of such management, including, during the conduct of operation of Incorporated forces.

The minimal time function associated with a collection of sets

We define the minimal time function associated with a collection of sets which is motivated by the optimal time problem for nonconvex constant dynamics. We first provide various basic properties of this new function: lower semicontinuity, principle of optimality, convexity, Lipschitz continuity, among others. We also compute and estimate proximal, Fréchet and limiting subdifferentials of the new function at points inside the target set as well as at points outside the target. An application to location problems is also given.

The human and the technical world: the ecological vector of philosophical comprehension

Under technicalization of practically all aspects of a person’s life and the vital world, the ecology of a person’s direct experience of their relations with all elements of the world is a problem both in the real existence of modern man and in theoretical knowledge about him. The article presents the experience of philosophical reflection necessary for finding the optimal way to solve a number of fundamental issues that have become relevant again: How is a person possible in a technical world? What is the general (i.e. philosophical — as a general level of understanding) basis of human relations with the technicalized world? How is knowledge about man possible and what should it be like in the new conditions of the technical world? A person in the technical world is possible as a person, so it is necessary to develop and strengthen the ecological way of their relations, to preserve / reproduce them as relations between the natural and the artificial, the «living» and the «nonliving». The ecological approach is based on the logic of the inter-proportionality of man and the world, on maintaining proportionality, correlating the possibilities of full reproduction and development of each of the «origins» — the human and the technical — in their orientation towards each other. It is based on the principle of optimality in relations between the parties, when there are created the best opportunities for development and realization of each of the parties’ internal potential. The ecological approach has a methodological significance in theoretical and practical senses: it can be considered both as an approach in theoretical research and as an approach to organizing and implementing practical relations of a person with the technical world.

The Principle of Least Action As Universal Principle of Productive Housekeeping

Any economic system is based on the analysis of the alternative development options existing in these conditions and the choice of the optimal one. In this case, the following question is fundamental: what principle of optimality should one be guided in when deciding on the choice of the option of carrying out economic activity. In this paper, it is proposed to use the Principle of Least Action (PLA) as such a principle. When applying this principle in practice, the goals of economic activity are achieved and the available resources are rationally used: the total costs of living and past (materialized) labor are minimized. The implementation of the PLA contributes to an increase in both the productivity of living labor and the productivity of aggregate labor. When used in practice PLA solves the problem of replacing manual labor machine. In this case, first of all, the release of heavy physical labor from economic activity takes place.