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1
Content available remote A multiple criteria decision making method base on relative value distances
Shyur H., Yin L., Shih H., Cheng C.
Foundations of Computing and Decision Sciences
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2015
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Vol. 40, No. 4
299--315
EN
This paper proposes a new multiple criteria decision-making method called ERVD (election based on relative value distances). The s-shape value function is adopted to replace the expected utility function to describe the risk-averse and risk-seeking behavior of decision makers. Comparisons and experiments contrasting with the TOPSIS (Technique for Order Preference by Similarity to the Ideal Solution) method are carried out to verify the feasibility of using the proposed method to represent the decision makers’ preference in the decision making process. Our experimental results show that the proposed approach is an appropriate and effective MCDM method.
2
Content available Sequential optimization for semilinear divergent hyperbolic equation with a boundary control and state inequality constraint
Gavrilov V. S., Sumin M. I.
Control and Cybernetics
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2014
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Vol. 43, no. 2
183--226
EN
An optimal control problem with a state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind is considered. The state constraint contains a functional parameter that belongs to the class of continuous functions and occurs as an additive term. We study the properties of solutions of linear hyperbolic equations in divergence form with measures in the original data and compute the first variations of functionals on the basis of a so-called two-parameter needle variation of controls. We consider the necessary conditions for minimizing sequences in an optimal control problem with a pointwise in time state constraint of inequality type and with dynamics described by a semilinear hyperbolic equation in divergence form with the non-homogeneous boundary condition of the third kind. For the parametric optimization problem, we also consider regularity and normality conditions stipulated by the differential properties of its value function.
3
Content available Remarks on solutions of equations with absolute value function
Major J., Powązka Z.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2011
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Vol. 16
249--254
EN
In this paper, we give the proposition of didactic discussion on the existence of solutions of some equations containing expressions with absolute value. We are interested in the possibility of applying the method of conceptual problem solving. Under this term we understand such a procedure, in which the solver is not limited to the automatic application of the definition of the absolute value, but he can reject some cases based on his mathematical knowledge. To do this, one must make use from various features of this concept - not only from its definition.
4
Content available remote A deterministic approach to the Skorokhod problem
Bettiol P.
Control and Cybernetics
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2006
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Vol. 35, no 4
787-802
EN
We prove an existence and uniqueness result for the solutions to the Skorokhod problem on uniformly prox-regular sets through a deterministic approach. This result can be applied in order to investigate some regularity properties of the value function for differential games with reflection on the boundary.
5
Content available remote A Method for Constructing ε-value Functions for The Bolza Problem of Optimal Control
Pustelnik J.
International Journal of Applied Mathematics and Computer Science
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2005
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Vol. 15, no 2
177-186
EN
The problem considered is that of approximate minimisation of the Bolza problem of optimal control. Starting from Bellman's method of dynamic programming, we define the ε-value function to be an approximation to the value function being a solution to the Hamilton-Jacobi equation. The paper shows an approach that can be used to construct an algorithm for calculating the values of an ε-value function at given points, thus approximating the respective values of the value function.
6
Content available remote Koncepcja ogólnej oceny cyklu życia obiektu infrastruktury z zastosowaniem metod optymalizacji wielokryterialnej
Truchanowicz T.
Biuletyn Wojskowej Akademii Technicznej
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2004
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Vol. 53, nr 8
73--89
PL
Przedstawiono koncepcję ogólnej oceny cyklu życia obiektu infrastruktury jako metody wielokryterialnego wspomagania decyzji wyboru wariantu. Sformułowano odpowiedni problem analizy wieloatrybutowej oraz zaproponowano rozwiązanie tego problemu za pomocą maksymalizacji funkcji użyteczności lub addytywnej funkcji kompromisu.
EN
A conception of life cycle total assessment of an infrastructure object as the conception of multiple criteria decision making method, is presented in this paper. The method concerns selection of an infrastructure variant. An appropriate problem of the multiattributive analysis is formulated. Solution of this problem by means of maximization of value function or the additive compromise function is also proposed.
7
Content available On the value function for multi-isotope mixtures separation
Palkin V. A.
Ars Separatoria Acta
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2004
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No. 3
51-61
EN
One of the possible approaches to the introduction of the value function in the case of multi-isotope mixtures is presented. It is based on a simplified model of separation processes in cascades and elements with multiplication of elementary effects of separation. A differential equation, being a necessary condition of the determination of the value function, is derived from the analysis of this model. Its general solution contains arbitrary constants which should be obtained considering boundary conditions and specific features of the separation process. Additional conditions concerning use of the found solutions in cascade criteria of an estimation of separation efficiency are stipulated. The applicability of various kinds of the value function forming at different conditions is analyzed. The forms of the value function which reflect best the optimal cascade with assigned external concentrations of the desired isotope and the matched abundance ratio cascade (MARC) are established.
8
Content available Finite-dimensional representations of the value functions of some optimal control problems
Mirica S.
Control and Cybernetics
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2002
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Vol. 31, no 3
779-801
EN
In this survey we analyze the possibility of obtaining information on regularity and irregularity properties of the value functions of some optimal control problems from their more precise description as marginal functions of finite-dimensional type, in terms of certain "generalized characteristic flows" which, in turn, may be constructed using either necessary optimality conditions (PMP-Pontryagin's Minimum Principle), whenever applicable, or suitable extensions of Cauchy's Method of Characteristics for the associated Hamilton-Jacobi-Bellman equation. This type of representation, which may be justified either by the application of PMP "combined" with existence theorems or by the application of a suitable verification theorem of Dynamic Programming type, not only facilitates numerical computation of the value function but also may allow identification of its discontinuity points, non-differentiability points, propagation of singularities, etc. ; this approach is illustrated with three significant examples from classical Calculus of Variations.
9
Content available Optimal control of semilinear elliptic equation with state constraint : maximum principle for minimizing sequence, regularity, normality, sensitivity
Sumin M.
Control and Cybernetics
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2000
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Vol. 29, no 2
449-472
EN
This article deals with state constrained optimal control problem for semilinear elliptic equation in a domain Omega. The state constraint is lumped on the compactum X contained in/implied by Omega n and contains a functional parameter q in C(X ). It is shown that any minimizing approximate solution (m.a.s.) in the sense of J. Warga satisfies the pointwise maximum principle (the maximum principle for m.a.s.) if the problem is meaningful, i.e., the value of the problem is finite. It is also shown that a condition of Slater's type is sufficient for the normality in the so-called "linear-convex" problem, and the normality of the problem for some fixed value of the parameter q in C(X ) implies the Lipschitz continuity of its value function in a neighborhood of q. The paper contains illustrative examples.
10
Content available remote Problemy stosowania teorii użyteczności w optymalizacji gospodarowania odpadami
Truchanowicz T.
Biuletyn Wojskowej Akademii Technicznej
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2000
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Vol. 49, nr 10
73-87
PL
Omówiono problemy zależności pomiędzy kryteriami oceny wariantów oraz procedurę określania odpowiedniej postaci funkcji użyteczności (w warunkach pewności). Zaproponowano metodę wielokryterialnego wspomagania decyzji w zakresie gospodarowania odpadami, polegającą na maksymalizacji addytywnej funkcji kompromisu.
EN
In this paper are discussed some problems resulting from mutual dependences between options assessment criteria and a procedure for finding a suitable from of value function, A method for multicriteria supporting decision making in the range of waste management is also proposed. This method consists in maximization of the additive compromise function.
11
Content available remote Relaxing constrained control systems
Frankowska H., Rampazzo F.
Bulletin of the Polish Academy of Sciences. Mathematics
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1998
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Vol. 46, no 1
70-81
EN
In this paper we provide a relaxation result for control systems under both equality and inequality constraints involving the state and the control. In particular we show that the Mangasarian-Fromowitz constraint qualification allows to rewrite constrained systems as differential inclusions with locally Lipschitz right-hand side. Then Filippov-Ważewski relaxation theorem may be applied to show that ordinary solutions are dense in the set of relaxed solutions. If, besided agreeing with the above constraints, the state has to remain in a control-independent set K, then we provide a condition on the feasible velocities on the boundary of K to get a relaxation theorem.
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