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Tytuł:
Sufficient conditions for optimality for a mathematical model of drug treatment with pharmacodynamics
Autorzy:
Leszczynski, M.
Ratajczyk, E.
Ledzewicz, U.
Schättler, H.
Powiązania:
https://bibliotekanauki.pl/articles/255130.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
optimal control
sufficient conditions for optimality
method of characteristics
pharmacodynamic model
Opis:
We consider an optimal control problem for a general mathematical model of drug treatment with a single agent. The control represents the concentration of the agent and its effect (pharmacodynamics) is modelled by a Hill function (i.e., Michaelis-Menten type kinetics). The aim is to minimize a cost functional consisting of a weighted average related to the state of the system (both at the end and during a fixed therapy horizon) and to the total amount of drugs given. The latter is an indirect measure for the side effects of treatment. It is shown that optimal controls are continuous functions of time that change between full or no dose segments with connecting pieces that take values in the interior of the control set. Sufficient conditions for the strong local optimality of an extremal controlled trajectory in terms of the existence of a solution to a piecewise defined Riccati differential equation are given.
Źródło:
Opuscula Mathematica; 2017, 37, 3; 403-419
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
P-order necessary and sufficient conditions for optimality in singular calculus of variations
Autorzy:
Prusińska, Agnieszka
Tret'yakov, Alexey
Powiązania:
https://bibliotekanauki.pl/articles/729251.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
singular variational problem
necessary condition of optimality
p-regularity
p-factor operator
Opis:
This paper is devoted to singular calculus of variations problems with constraint functional not regular at the solution point in the sense that the first derivative is not surjective. In the first part of the paper we pursue an approach based on the constructions of the p-regularity theory. For p-regular calculus of variations problem we formulate and prove necessary and sufficient conditions for optimality in singular case and illustrate our results by classical example of calculus of variations problem.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2010, 30, 2; 269-279
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal Control for a Class of Compartmental Models in Cancer Chemotherapy
Autorzy:
Świerniak, A.
Ledzewicz, U.
Schättler, H.
Powiązania:
https://bibliotekanauki.pl/articles/908158.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
medycyna
matematyka
compartmental models
cancer chemotherapy
optimal control
necessary and sufficient conditions for optimality
Opis:
We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models B and C, are analyzed, which consider a blocking agent and a recruiting agent, respectively. In Model B a blocking agent which slows down cell growth during the synthesis allowing in consequence the synchronization of the neoplastic population is added. In Model C the recruitment of dormant cells from the quiescent phase to enable their efficient treatment by a cytotoxic drug is included. In all models the cumulative effect of the killing agent is used to model the negative effect of the treatment on healthy cells. For each model it is shown that singular controls are not optimal. Then sharp necessary and sufficient optimality conditions for bang-bang controls are given for the general class of models P and illustrated with numerical examples.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 3; 357-368
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sufficient optimality conditions for multivariable control problems
Autorzy:
Nowakowski, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/729408.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
sufficient optimality condition
wave equations
parbolic equation
elliptic equation
Dirichlet boundary controls
dual dynamic programming
Opis:
We study optimal control problems for partial differential equations (focusing on the multidimensional differential equation) with control functions in the Dirichlet boundary conditions under pointwise control (and we admit state - by assuming weak hypotheses) constraints.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 1; 135-150
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dual sufficient optimality conditions for optimal control
Autorzy:
Młynarska, E.
Powiązania:
https://bibliotekanauki.pl/articles/205961.pdf
Data publikacji:
2001
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
minimum względne
nierówność podwójna Hamiltona-Jacobiego
zagadnienie sterowania optymalnego
dual Hamilton-Jacobi inequality
dual sufficient optimality conditions
optimal control problem
relative minimum
Opis:
In this paper we develop the first and second order dual sufficient optimality conditions for a nonlinear optimal control problem. Our conditions are derived from the dual Hamilton-Jacobi approach applied to the generalized problem of Bolza. We do not require neither any convexity on the data, nor that the control set U be polyhedral, nor that the control function be in the interior of U. Instead, we assume the existence of a function which satisfies a certain inequality.
Źródło:
Control and Cybernetics; 2001, 30, 1; 45-54
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sufficient conditions of optimality for multiobjective optimization problems with γ-paraconvex data
Autorzy:
Amahroq, T.
Taa, A.
Powiązania:
https://bibliotekanauki.pl/articles/1219613.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
contingent derivative
γ-paraconvex multifunction
optimality conditions
B-tangentially compact
compactly γ-paraconvex multifunction
Pareto minimal point
Opis:
We study multiobjective optimization problems with γ-paraconvex multifunction data. Sufficient optimality conditions for unconstrained and constrained problems are given in terms of contingent derivatives.
Źródło:
Studia Mathematica; 1997, 124, 3; 239-247
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Second derivatives and sufficient optimality conditions for shape funetionals
Autorzy:
Eppler, K.
Powiązania:
https://bibliotekanauki.pl/articles/206712.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal shape design
second directional derivatives
sufficient optimality conditions
Opis:
For sorne heuristic approaches to boundary variation in shape optimization the computation of second derivatives of domain and boundary integral functionals, their symmetry and a comparison to the velocity field or material derivative method are discussed. Moreover, for these approaches the functionals are Frechet-differentiable in some sense, because at least a local embedding into a Banach space problem is possible. This allows the discussion of sufficient condition in terms of a coercivity assumption on the second Frechet-derivative. The theory is illustrated by a discussion of the famous Dido problem.
Źródło:
Control and Cybernetics; 2000, 29, 2; 485-511
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On localizing global Pareto solutions in a given convex set
Autorzy:
Drwalewska, Agnieszka
Gajek, Lesław
Powiązania:
https://bibliotekanauki.pl/articles/1338686.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
sufficient and necessary conditions for optimality
Pareto optimal solutions
dual cones
feasible directions
Opis:
Sufficient conditions are given for the global Pareto solution of the multicriterial optimization problem to be in a given convex subset of the domain. In the case of maximizing real valued-functions, the conditions are sufficient and necessary without any convexity type assumptions imposed on the function. In the case of linearly scalarized vector-valued functions the conditions are sufficient and necessary provided that both the function is concave and the scalarization is increasing with respect to the cone generating the preference relation.
Źródło:
Applicationes Mathematicae; 1999, 26, 4; 383-394
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sufficient optimality conditions for a bang-singular extremal in the minimum time problem
Autorzy:
Poggiolini, L.
Stefani, G.
Powiązania:
https://bibliotekanauki.pl/articles/969613.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
minimum time
second order sufficient conditions
bang-singular arc
Hamiltonian formalism
Opis:
The paper gives second order sufficient conditions for the strong local optimality of a bang-singular extremal in a minimum time problem. The conditions are given in terms of regularity assumptions on the extremal and of the coercivity of the extended second variation associated to the minimum time problem with fixed end-points on the singular arc. The conditions are close to the necessary ones in the usual sense, namely we require strict inequalities where necessary conditions have mild inequalities.
Źródło:
Control and Cybernetics; 2008, 37, 2; 469-490
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of pandemic with game methodology and numerical approximation
Autorzy:
Matusik, Radosław
Nowakowski, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/29432416.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
COVID-19
game model of pandemic
approximate dual dynamic programming
sufficient approximate optimality conditions for Nash equilibrium
numerical algorithm
Opis:
We build a mathematical game model of pandemic transmission, including vaccinations of population and budget costs of different acting to eliminate pandemic. We assume the interactions among different groups: vaccinated, susceptible, exposed, infectious, super-spreaders, hospitalized and fatality, defining a system of ordinary differential equations, which describes compartment model of disease and costs of the treatment. The goal of the game is to describe the development disease under different types of treatment, but including costs of them and social restrictions, during the shortest time period. To this effect we construct a dual dynamic programming method to describe open-loop Nash equilibrium for treatment, a group of people having antibodies and budget costs. Next, we calculate numerically an approximate open-loop Nash equilibrium.
Źródło:
Archives of Control Sciences; 2023, 33, 3; 651--680
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Second order optimality conditions for bang-bang control problems
Autorzy:
Maurer, H.
Osmolovskii, N. P.
Powiązania:
https://bibliotekanauki.pl/articles/970524.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie przekaźnikowe
bang-bang control
second order necessary and sufficient conditions
critical cone
transformation of quadratic forms
numerical verification of second order conditions
van der Pol oscillator
Opis:
Second order necessary and sufficient optimality conditions for bang-bang control problems have been studied in Milyutin, Osmolovskii (1998). These conditions amount to testing the positive (semi-)definiteness of a quadratic form on a critical cone. The assumptions are appropriate for numerical verification only in some special cases. In this paper, we study various transformations of the quadratic form and the critical cone which will be tailored to different types of control problems in practice. In particular, by means of a solution to a linear matrix differential equation, the quadratic form can be converted to perfect squares. We demonstrate by three practical examples that the conditions obtained can be verified numerically.
Źródło:
Control and Cybernetics; 2003, 32, 3; 555-584
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Equivalence of second order optimality conditions for bang-bang control problems. Part 1: Main results
Autorzy:
Osmolovskii, N. P.
Maurer, H.
Powiązania:
https://bibliotekanauki.pl/articles/970559.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie przekaźnikowe
stożek krytyczny
forma kwadratowa i równoważność
bang-bang control
second order necessary and sufficient conditions
critical cone
Opis:
Second order optimality conditions have been derived in the literature in two different forms. Osmolovskii (1988a, 1995, 2000, 2004) obtained second order necessary and sufficient conditions requiring that, a certain quadratic form be positive (semi)-definite on a critical cone. Agrachev, Stefani, Zezza (2002) first, reduced the bang-bang control problem to finite-dimensional optimization and then show that well-known sufficient optimality conditions for this optimization problem supplemented by the strict bang-bang property furnish sufficient conditions for the bang-bang control problem. In this paper, we establish the equivalence of both forms of sufficient conditions and give explicit relations between corresponding Lagrange multipliers and elements of critical cones. Part 1 summarizes the main results while detailed proofs will be given in Part 2.
Źródło:
Control and Cybernetics; 2005, 34, 3; 927-950
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sufficient optimality criteria and duality for multiobjective variational control problems with B-(p,r)-invex function
Autorzy:
Antczak, T.
Jimenez, M. A.
Powiązania:
https://bibliotekanauki.pl/articles/255711.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
multiobjective variational control problems
efficient solution
B-(p, r)-invex functions
optimality conditions
duality
Opis:
In this paper, we generalize the notion of B-(p, r)-invexity introduced by Antczak in [A class of B-(p; r)-invex functions and mathematical programming, J. Math. Anal. Appl. 286 (2003), 187–206] for scalar optimization problems to the case of a multiobjective variational programming control problem. For such nonconvex vector optimization problems, we prove sufficient optimality conditions under the assumptions that the functions constituting them are B-(p, r)-invex. Further, for the considered multiobjective variational control problem, its dual multiobjective variational control problem in the sense of Mond-Weir is given and several duality results are established under B-(p, r)-invexity.
Źródło:
Opuscula Mathematica; 2014, 34, 4; 665-682
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Necessary and sufficient conditions for a Pareto optimal allocation in a discontinuous Gale economic model
Autorzy:
Michalak, A.
Studniarski, M.
Powiązania:
https://bibliotekanauki.pl/articles/255729.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Gale model
discontinuous functions
generalized directional derivatives
higher-order conditions
Pareto optimality
Opis:
In this paper we examine the concept of Pareto optimality in a simplified Gale economic model without assuming continuity of the utility functions. We apply some existing results on higher-order optimality conditions to get necessary and sufficient conditions for a locally Pareto optimal allocation.
Źródło:
Opuscula Mathematica; 2014, 34, 4; 827-835
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kuhn-Tucker type optimality conditions for some class of nonsmooth programming problems
Autorzy:
Śmietański, M. J.
Powiązania:
https://bibliotekanauki.pl/articles/206291.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
pochodna Diniego
pochodna Clarka
wypukłość uogólniona
liniowość uogólniona
warunki konieczne i wystarczające optymalności
nonsmooth programming
Dini derivative
Clarke derivative
generalized convexity
generalized linearity
necessary and sufficient optimality conditions
Opis:
We consider two nonlinear programming problems with nonsmooth functions. The necessary and sufficient first order optimality conditions use the Dini and Clarke derivatives. However, the obtained Kuhn-Tucker conditions have a rather classical form. The sufficient conditions alone are obtained thanks to some properties of generalized convexity and generalized linearity of functions. The necessary and sufficient optimality conditions are given in the Lagrange form.
Źródło:
Control and Cybernetics; 2003, 32, 2; 361-376
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 20

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