Kyösti Tarvainen

Kyösti Tarvainen
Aalto University · Department of Mathematics and Systems Analysis

Doctor of Engineering

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15
Publications
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63
Citations

Publications

Publications (15)
Article
Full-text available
The ethnic and religious compositions of Nordic populations have been projected by Eurostat (Lanzieri, 2011), the Pew Research Center (2015), and Statistics Denmark (2015). These studies are updated and complemented in this paper. Lanzieri’s consideration of the native population is supplemented by taking into account assimilation via marriages bet...
Article
This paper addresses the forming of integral expressions such as by differential or infinitesimal derivations. A rigorous justification of these handy informal derivations is a major pedagogical problem in calculus. In this paper, checks are presented by which one can usually verify–with clear geometrical and physical considerations–that integral e...
Article
The study addresses the problem of how to present the setting up of definite integrals of real functions like J af(x) dx. In modelling, infinitesimal considerations dating back to the less rigorous times of calculus are still successfully used. On the other hand, students are given a rigorous definition of the definite integral in the calculus cour...
Article
In this paper, a simple elimination condition is introduced that may help in the verification or falsification of the principle of optimality and in deriving rigorously dynamic programming algorithms. Through two examples of single objective optimization, it is shown how the elimination condition can be used to rigorously derive dynamic programming...
Article
This article is of a pedagogical nature, presenting various results of calculus that can be used when differential equation models are derived as rigorously as possible. The purpose of the paper is to present a new student of mathematical modelling with approaches which can be seen as more rigorous versions of the usual infinitesimal derivations.
Article
An interactive negotiation procedure for large scale systems with multiple objectives is proposed. It is assumed that there are multiple decision-makers, who have their own multiple objectives and who are dependent on each other via common resources or physical connections. The negotiation procedure includes two repeated main steps: the decision-ma...
Article
An interactive negotiation procedure for large scale systems with multiple objectives is proposed. It is assumed that there are multiple decision makers, who have their own multiple objectives and who are dependent on each other via common resources or physical connections. The negotiation procedure includes two repeated main steps: the decision ma...
Article
Basic issues concerning Pareto optimal (noninferior) alternatives in large scale decomposable systems are considered. The mathematical models are supposed to consist of interconnected subsystems with multiple objectives in each. The overall objectives are functions of the subsystem objectives. Three different cases with respect to the number of dec...
Article
An iterative negotiation procedure for multiple decision makers, who have their own multiple objectives and who are depended on each other via common resources or physical connections, is proposed. The scheme includes two repe ated basic steps : the decision makers' independent multicriteria optimizations of their subsystems and a convenient step f...
Article
People who are not familiar with the multicriteria optimization theory often deal with multicriteria problems in the following way. One objective is taken as a single criteria to be optimized and some limits are set for the values of the other objectives. That is, the other objectives are treated as constraints in an ordinary optimization problem....
Article
General nonfeasible (price-coordination, interaction balance) hierarchical optimization algorithms for large-scale systems with multiple objectives are considered. The systems studied consist of connected subsystems with multiple objectives (subgoals, indicators); the overall objectives are functions of the subsystem objectives. It is shown that, u...
Article
Decomposition methods for multicriteria dynamic (discrete-time) problems are derived. In these methods, the original problem is reduced to a series of multicriteria subproblems related to individual stages. Hence, the dimensionality of decision variables in each subproblem is smaller than in the original problem. The following decomposition procedu...
Article
A static deterministic hierarchical system consisting of subsystems with multiple objectives is considered here; this system's overall multiple objectives are functions of its subsystems' objectives. Two powerful and well-developed approaches¿the hierarchical multilevel and the multiobjective multiattribute approaches¿are integrated into a unifie...
Article
Decomposition methods for multicriteria dynamic (discrete time) problems are derived. In these methods, the original problem is reduced to a series of multicriteria subproblems related to individual stages. Hence, the dimensionality of decision-variables in each subproblem is smaller than in the original problem. In a general case where the objecti...
Chapter
This paper addresses the integration of the hierarchical and multi-objective approaches into a unified framework. Several facets of theoretical and methodological aspects of the proposed hierarchical-multiobjective framework are discussed. The Surrogate Worth Trade-Off (SWT) method — a multiobjective optimization method — which is used as the basis...

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