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Wyświetlanie 1-15 z 23
Tytuł:
Systems of variational inequalities related to economic equilibrium
Autorzy:
Naniewicz, Z.
Nockowska, M.
Powiązania:
https://bibliotekanauki.pl/articles/970931.pdf
Data publikacji:
2007
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimization problem
variational inequalities
duality
Opis:
In the paper a new approach to the Walrasian general equilibrium model of economy is presented. The classical market clearing condition is replaced by suitably formulated variational inequality. It states that the market clears for a commodity if its equilibrium price is positive; otherwise, there may be an excess supply of the commodity in equilibrium and then its price is zero. Such approach enables establishing new existence results without assumptions which were fundamental for the currently used methods: (i) Dis-utility functions are not required to be strictly convex and they may attain their minima in the consumption sets (the local nonsatiation of preferences is not required). (ii) The boundary of the positive orthant is allowed for the price vector in equilibrium. It allows for investigation of certain new problems, e.g. bankruptcy conditions.
Źródło:
Control and Cybernetics; 2007, 36, 4; 889-909
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on a Fenchel-Young type conjugacy for convexifiable functions
Autorzy:
Galewski, M.
Powiązania:
https://bibliotekanauki.pl/articles/971047.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
dualność Fechnela-Younga
convexifiability
Fenchel-Young duality
Opis:
We provide definition of such a Fenchel-Young type duality for a convexifiable function f that its second dual is a given function f. Examples and possible applications are given.
Źródło:
Control and Cybernetics; 2003, 32, 2; 377-381
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Control and optimization of abstract continuous time evolution inclusions
Autorzy:
Mokhtar-Kharroubi, Hocine
Powiązania:
https://bibliotekanauki.pl/articles/31342761.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
evolution inclusion
well-posedness
optimal control
strong duality
system of optimality
Fenchel duality
convex process of evolution
integrodifferential inclusions
Opis:
Abstract controlled evolution inclusions are revisited in the Banach spaces setting. The existence of solution is established for each selected control. Then, the input–output (or, control-states) multimap is examined and the Lipschitz continuous well posedness is derived. The optimal control of such inclusions handled in terms of a Bolza problem is investigated by means of the so-called PF format of optimization. A strong duality is provided, the existence of an optimal pair is given and the system of optimalty is derived. A Fenchel duality is built and applied to optimal control of convex process of evolution. Finally, it will be shown how the general theory we provided can be applied to a wide class of controled integrodifferental inclusions.
Źródło:
Control and Cybernetics; 2023, 52, 1; 5-34
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized α-V-univex functions for multiobjective variational control problems
Autorzy:
Sharma, S.
Choudhury, S.
Jayswal, A.
Powiązania:
https://bibliotekanauki.pl/articles/206848.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
control problem
α-V-univexity
efficiency
sufficiency
duality
Opis:
The purpose of this paper is to introduce a new class of _-V-univex/ generalized _-V-univex functions for a class of multiobjective variational control problems. Moreover, sufficient optimality conditions and Mond-Weir type duality results, associated with the multiobjective variational control problem, are established under aforesaid assumptions.
Źródło:
Control and Cybernetics; 2014, 43, 3; 403-420
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sufficient optimality condition and duality of nondifferentiable minimax ratio constraint problems under (p, r)-ρ-(η, θ)-invexity
Autorzy:
Kailey, Navdeep
Sethi, Sonali
Saini, Shivani
Powiązania:
https://bibliotekanauki.pl/articles/2183486.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
minimax fractional programming
optimality conditions
duality
generalized invexity
Opis:
There are several classes of decision-making problems that explicitly or implicitly prompt fractional programming problems. Portfolio selection problems, agricultural planning, information transfer, numerical analysis of stochastic processes, and resource allocation problems are just a few examples. The huge number of applications of minimax fractional programming problems inspired us to work on this topic. This paper is concerned with a nondifferentiable minimax fractional programming problem. We study a parametric dual model, corresponding to the primal problem, and derive the sufficient optimality condition for an optimal solution to the considered problem. Further, we obtain the various duality results under (p, r)-ρ-(η, θ)-invexity assumptions. Also, we identify a function lying exclusively in the class of (−1, 1)-ρ-(η, θ)- invex functions but not in the class of (1,−1)-invex functions and convex function already existing in the literature. We have given a non-trivial model of nondifferentiable minimax problem and obtained its optimal solution using optimality results derived in this paper.
Źródło:
Control and Cybernetics; 2022, 51, 1; 71--88
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimality conditions and a classification of duality schemes in vector optimization
Autorzy:
El Ghali, B.
Powiązania:
https://bibliotekanauki.pl/articles/205741.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
dwoistość
optymalizacja wektorowa
duality
existential solutions
minimality
vector optimization
Opis:
Vector minimization of a relation F valued in an ordered vector space under a constraint A consists in finding x[0] belongs to A, w[0] belongs to Fx[0] such that w[0] is minimal in FA. To a family of vector minimization problems minimize[x belongs to X] F(x, y), y [belongs to] Y, one associates a Lagrange relation [L(x, [xi], y[0]) = union of sets y belongs to Y(F(x, y)-xi(y)+(y[0]))] where [xi] belongs to an arbitrary class [Xi] of mappings. For this type of problem, there exist several notions of solutions. Some useful characterizations of existential solutions are established and, consequently, some necessary conditions of optimality are derived. One result of intermediate duality is proved with the aid of the scalarization theory. Existence theorems for existential solutions are given and a comparison of several exact duality schemes is established, more precisely in the convex case it is shown that the majority of exact duality schemes can be obtained from one result of S. Dolecki and C. Malivert.
Źródło:
Control and Cybernetics; 2000, 29, 4; 839-860
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Higher order efficiency and duality for multiobjective variational problem
Autorzy:
Kumar, P.
Sharma, B.
Powiązania:
https://bibliotekanauki.pl/articles/206150.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
higher order duality
variational problem
efficiency of higher order
Opis:
In this paper, multiobjective variational programming problem is considered. Mond-Weir type higher order duality results are established by using the efficiency of higher order as the optimization tool. In order to prove these results, we propose the notion of generalized higher order (F,ρ,θ,m,h)−invexity.
Źródło:
Control and Cybernetics; 2017, 46, 2; 137-145
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonconvex minimization related to quadratic double-well energy - approximation by convex problemsenergy – approximation by convex problems
Autorzy:
Naniewicz, Z.
Puchała, P.
Powiązania:
https://bibliotekanauki.pl/articles/205686.pdf
Data publikacji:
2012
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
nonconvex integrand
minimum of convex functions
duality
parameterized Young measures
Opis:
A double-well energy expressed as a minimum of two quadratic functions, called phase energies, is studied taking into account minimization of the corresponding integral functional. Such integral, as being not sequentially weakly lower semicontinuous, does not admit classical minimizers. To derive the relaxation formula for the infimum, the appropriate minimizing sequence is constructed. It consists of solutions of some approximating convex problems involving characteristic functions related to the phase energies. The weak limit of this sequence and the weak limit of the sequence of solutions of dual problems combined with the weak-star limits of the characteristic functions related to the phase energies allow to establish the final relaxation formula. It is also shown that infimum can be expressed by the Young measure associated with constructed minimizing sequence. An explicit form of Young measure in some regions of the involved domain is calculated.
Źródło:
Control and Cybernetics; 2012, 41, 3; 525-543
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Set-valued minimax fractional programming problems under -cone arcwise connectedness
Autorzy:
Das, Koushik
Powiązania:
https://bibliotekanauki.pl/articles/2183488.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
convex cone
set-valued map
contingent epiderivative
arcwise connectedness
duality
Opis:
In this paper, we consider a set-valued minimax fractional programming problem (MFP), where the objective as well as constraint maps are set-valued. We introduce the notion of ρ- cone arcwise connectedness of set-valued maps as a generalization of cone arcwise connected set-valued maps. We establish the sufficient Karush-Kuhn-Tucker (KKT) conditions for the existence of minimizers of the problem (MFP) under ρ-cone arcwise connectedness assumption. Further, we study the Mond-Weir (MWD), Wolfe (WD), and mixed (MD) types of duality models and prove the corresponding weak, strong, and converse duality theorems between the primal (MFP) and the corresponding dual problems under ρ-cone arcwise connectedness assumption.
Źródło:
Control and Cybernetics; 2022, 51, 1; 43--69
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximating the solution of a dynamic, stochastic multiple knapsack problem
Autorzy:
Hartman, J. C.
Perry, T. C.
Powiązania:
https://bibliotekanauki.pl/articles/970874.pdf
Data publikacji:
2006
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
programowanie liniowe
dualność
stochastic dynamic programming
approximate dynamic programming
linear programming
duality
Opis:
We model an environment where orders arrive probabilistically over time, with their revenues and capacity requirements becoming known upon arrival. The decision is whether to accept an order, receiving a reward and reserving capacity, or reject an order, freeing capacity for possible future arrivals. We model the dynamic, stochastic multiple knapsack problem (DSMKP) with stochastic dynamic programming (SDP). Multiple knapsacks are used as orders may stay in the system for multiple periods. As the state space grows exponentially in the number of knapsacks and the number of possible orders per period, we utilize linear programming and duality to quickly approximate the end-of-horizon values for the SDP. This helps mitigate end-of-study effects when solving the SDP directly, allowing for the solution of larger problems and leading to increased quality in solutions.
Źródło:
Control and Cybernetics; 2006, 35, 3; 535-550
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Second-order optimality conditions in nonsmooth vector optimization
Autorzy:
Yadav, Priyanka
Powiązania:
https://bibliotekanauki.pl/articles/31342762.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
vector optimization
cones
nonsmooth second-order cone-convexity
second-order optimality
duality
Opis:
In this paper, we introduce new classes of nonsmooth second-order cone-convex functions and respective generalizations in terms of first and second-order directional derivative. These classes encapsulate several already existing classes of cone-convex functions and their weaker variants. Second-order KKT type sufficient optimality conditions and duality results for a nonsmooth vector optimization problem are proved using these functions. The results have been supported by examples.
Źródło:
Control and Cybernetics; 2023, 52, 1; 35-51
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Multiobjective duality for the Markowitz portfolio optimization problem
Autorzy:
Wanka, G.
Powiązania:
https://bibliotekanauki.pl/articles/206011.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
dualność
optymalizacja
duality
expected return
investment
Markowitz model
optimality conditions
portfolio optimization
Opis:
The classical Markowitz approach to portfolio selection leads to a biobjective optimization problem where the objectives are the expected return and the variance of a portfolio. In this paper a biobjective dual optimization problem to the Markowitz portfolio optimization problem is introduced and analyzed. For the Markowitz problem and its dual, weak and strong vector duality assertions are derived. The optimality conditions are also verified.
Źródło:
Control and Cybernetics; 1999, 28, 4; 691-702
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On some optimization problem related to economic equilibrium
Autorzy:
Naniewicz, Z.
Powiązania:
https://bibliotekanauki.pl/articles/1839186.pdf
Data publikacji:
2002
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
dwoistość
nierówność wariacyjna
problem optymalizacji
równowaga
duality
equilibrium
optimization problem
variational inequalities
Opis:
The paper considers an optimization problem in which the minima of a finite collection of objective functions satisfy some unilateral constraints and are linked together by a certain subdifferential relationship. The governing relations are stated as a variational inequality defined on a nonconvex feasible set. By the reduction to the variational inequality involving nonmonotone multivalued mapping, defined over nonnegative orthant, the existence of solutions is examined. The prototype is the general economic equilibrium problem. The exemplification of the theory for the quadratic multi-objective function is provided.
Źródło:
Control and Cybernetics; 2002, 31, 1; 141-165
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Duality theory for state-constrained control problems governed by a first order PDE system
Autorzy:
Pickenhain, S.
Powiązania:
https://bibliotekanauki.pl/articles/205959.pdf
Data publikacji:
2002
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
teoria dwoistości
control problems with multiple integrals
duality theory
necessary and sufficient optimality conditions
Opis:
In this paper we prove weak and strong duality results for optimal control problems with multiple integrals, first-order partial differential equations and state constraints. We formulate conditions under which the sequence of canonical variables [y^epsilon] in the [epsilon]-maximum principle, proved in Pickenhain and Wagner (2000), form a maximizing sequence in the dual problem.
Źródło:
Control and Cybernetics; 2002, 31, 3; 833-845
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Convergence and extensions of variational problems with non-coercive functionals
Autorzy:
Ioffe, A.
Powiązania:
https://bibliotekanauki.pl/articles/206582.pdf
Data publikacji:
2002
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
duality
dwoistość
gamma-zbieżność
koercyjność
miara wektorowa
relaksacja
coercivity
Gamma-convergence
relaxation
vector measures
Opis:
The paper is a transcript of the lecture given at the European Symposium on Well-Posedness in Optimization in Warsaw. It contains a complete theory of variational problems with integrands not depending on x, including existence and relaxation theorems, a complete description of solutions and the connection between variational convergences of functionals and convergence of value functions and solutions of associated variational problems with the main emphasis on functionals that lack coercivity.
Źródło:
Control and Cybernetics; 2002, 31, 3; 507-519
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 23

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