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    Wyświetlanie 1-15 z 15
    Tytuł:
    Cone solutions of multi-order fractional difference systems
    Autorzy:
    Girejko, E.
    Mozyrska, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/206510.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    fractional difference operator
    fractional difference equation
    cone solutions
    Opis:
    The fractional difference system of equations with different fractional orders is considered. We obtain the existence and uniqueness results for the initial value problem. Cone solutions are presented. An example is given to illustrate the results.
    Źródło:
    Control and Cybernetics; 2013, 42, 2; 419-429
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the relaxation of state-constrained linear control problems via Henig dilating cones
    Autorzy:
    Kogut, P. I.
    Leugering, G.
    Schiel, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/206472.pdf
    Data publikacji:
    2016
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    optimal control
    state constrains
    relaxation
    Henig dilating cone
    optimality conditions
    Opis:
    We discuss a regularization of state-constrained optimal control problems via a Henig relaxation of ordering cones. Considering a state-constrained optimal control problem, the pointwise state constraint is replaced by an inequality condition involving a so-called Henig dilating cone. It is shown that this class of cones provides a reasonable solid approximation of the typically nonsolid ordering cones which correspond to pointwise state constraints. Thereby, constraint qualifications, which are based on the existence of interior points, can be applied to given problems. Moreover, we characterize admissibility and solvability of the original problem by analyzing the associated relaxed problem. We also show that the optimality system for the original problem can be obtained through the limit passage in the corresponding optimality system for the relaxed problem. As an example of our approach, we derive the optimality conditions for a state constrained Neumann boundary optimal control problem and show that in this case the corresponding Lagrange multipliers are more regular than Borel measures.
    Źródło:
    Control and Cybernetics; 2016, 45, 2; 131-162
    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:
    Φ- α(⋅)-K-monotone multifunctions with values in ordered Banach space with increasing norm
    Autorzy:
    Rolewicz, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/206769.pdf
    Data publikacji:
    2013
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    vector valued functions
    normal cone
    cone with bounded basis
    Φ-α(⋅)-K-subgradi-ents
    increasing norm
    Φ-α(⋅)-k-subdifferential Fréchet Φ-differentiability
    Opis:
    Let (X, d) be a metric space. Let Y be an ordered Banach space with increasing norm. Let Φ be a separable linear family (a class) of Lipschitz functions defined on X and with values in Y . Let α(⋅) be a nondecreasing function mapping the interwal [0,+∞) into itself such that limt↓0 α(t) / t = 0. We say that a multifunction mapping X into Φ is Φ -α(⋅)-K-monotone if for all k in the interior of K, k ∈ Int K, there is a constant Ck > 0 such that for all φx ∈Γ (x),φy ∈Γ (y) we have φx(x) + φy(y) − φx(y) − φy(x) ≥K −Ckα(d(x, y))k.It is shown in the paper that under certain conditions on each Φ - Φα(⋅)-K-monotone multifunction is single-valued and continuous on a dense G δ-set..
    Źródło:
    Control and Cybernetics; 2013, 42, 4; 793-803
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Weak sharp minima revisited Part I : basic theory
    Autorzy:
    Burke, J.
    Deng, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/206183.pdf
    Data publikacji:
    2002
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    dwoistość
    funkcja recesji
    ograniczenie błędu
    stożek recesji
    boundedly weak sharp minima
    duality
    error bounds
    normal cone inclusion
    recession cone
    recession function
    weak sharp minima
    Opis:
    The notion of sharp minima, or strongly unique local minima, emerged in the late 1970's as an important tool in the analysis of the perturbation behavior of certain classes of optimization problems as well as in the convergence analysis of algorithms designed to solve these problems. The work of Cromme and Polyak is of particular importance in this development. In the late 1980's Ferris coined the term weak sharp minima to describe the extension of the notion of sharp minima to include the possibility of a non-unique solution set. This notion was later extensively studied by many authors. Of particular note in this regard is the paper by Burke and Ferrris which gives an extensive exposition of the notion and its impact on convex programming and convergence analysis in finite dimensions. In this paper we build on the work of Burke and Ferris. Specifically, we generalize their work to the normed linear space setting, further dissect the normal cone inclusion characterization for weak sharp minima, study the asymptotic properties of weak sharp minima in terms of associated recession functions, and give new characterizations for local weak sharp minima and boundely weak sharp minima. This paper is the first of a two part work on this subject. In Part II, we study the links between the notions of weak sharp minima, bounded linear regularity, linear regularity, metric regularity, and error bounds in convex programming. Along the way, we obtain both new results and reproduce many existing results from a fresh perspective.
    Źródło:
    Control and Cybernetics; 2002, 31, 3; 439-469
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Necessary optimality conditions for a set valued fractional programming problem in terms of contingent epiderivatives
    Autorzy:
    Gadhi, A. N.
    Idrissi, M. El.
    Powiązania:
    https://bibliotekanauki.pl/articles/205692.pdf
    Data publikacji:
    2018
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    fractional optimization
    multi-objective optimization
    cone-convex mapping
    optimality conditions
    subdifferential
    Opis:
    In this paper, we are concerned with a multi-objective fractional extremal programming problem. Using the concept of subdifferential of cone-convex set valued mappings, introduced by Baier and Jahn (1999), together with the convex separation principle, we give necessary optimality conditions. An example illustrating the usefulness of our results is also provided.
    Źródło:
    Control and Cybernetics; 2018, 47, 2; 147-156
    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:
    Sensitivity analysis for state constrained optimal control problems
    Autorzy:
    Malanowski, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/206110.pdf
    Data publikacji:
    2011
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    sensitivity analysis
    cone-constrained optimization problems
    nonlinear optimal control
    first order state constraints
    Opis:
    A sensitivity result for cone-constrained optimization problem in abstract Hilbert spaces is obtained, using a slight modification of Haraux's theorem on differentiability of the metric projection onto polyhedric sets. This result is applied to sensitivity analysis for nonlinear optimal control problems subject to first order state constraints.
    Źródło:
    Control and Cybernetics; 2011, 40, 4; 1043-1058
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Second order conditions in optimal control problems with mixed equality-type constraints on a variable time interval
    Autorzy:
    Osmolovskii, N. P.
    Powiązania:
    https://bibliotekanauki.pl/articles/970741.pdf
    Data publikacji:
    2009
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    piecewise continuous control
    maximum principle
    second order necessary or sufficient conditions
    critical cone
    quadratic form
    Opis:
    This paper provides an analysis of second-order necessary or sufficient optimality conditions of Pontryagin or bounded strong minima, for optimal control problems of ordinary differential equations, considered on a nonfixed time interval, with constraints on initial-final time-state as well as mixed state-control constraints of equality type satisfying condition of linear independence of gradients w.r.t. control.
    Źródło:
    Control and Cybernetics; 2009, 38, 4B; 1535-1556
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Local cone approximations in optimization
    Autorzy:
    Castellani, M.
    Pappalardo, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/970281.pdf
    Data publikacji:
    2007
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    nonsmooth optimization
    cone approximations
    generalized directional epiderivatives
    optimality conditions
    constraint qualifications
    mean value theorem
    error bound
    Opis:
    We show how to use intensively local cone approximations to obtain results in some fields of optimization theory such as optimality conditions, constraint qualifications, mean value theorems and error bound.
    Źródło:
    Control and Cybernetics; 2007, 36, 3; 583-600
    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:
    Network optimality conditions
    Autorzy:
    Osmolovskii, Nikolai P.
    Qian, Meizhi
    Sokołowski, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/31343935.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    network
    optimal control problem
    weak local minimum
    Pontryagin’s maximum principle
    critical cone
    quadratic form
    second order optimality conditions
    Riccati equation
    Opis:
    Optimality conditions for optimal control problems arising in network modeling are discussed. We confine ourselves to the steady state network models. Therefore, we consider only control systems described by ordinary differential equations. First, we derive optimality conditions for the nonlinear problem for a single beam. These conditions are formulated in terms of the local Pontryagin maximum principle and the matrix Riccati equation. Then, the optimality conditions for the control problem for networks posed on an arbitrary planar graph are discussed. This problem has a set of independent variables xi varying within their intervals [0, li], associated with the corresponding beams at network edges. The lengths li of intervals are not specified and must be determined. So, the optimization problem is non-standard, it is a combination of control and design of networks. However, using a linear change of the independent variables, it can be reduced to a standard one, and we show this. Two simple numerical examples for the single-beam problem are considered.
    Źródło:
    Control and Cybernetics; 2023, 52, 2; 129-180
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A second-order sufficient condition for a weak local minimum in an optimal control problem with an inequality control constraint
    Autorzy:
    Osmolovskii, Nikolai P.
    Powiązania:
    https://bibliotekanauki.pl/articles/2183496.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    critical cone
    quadratic form
    first order tangent
    second order tangent
    second order optimality conditions
    weak local minimum
    inequality control constraint
    Pontryagin’s maximum principle
    Opis:
    This paper is devoted to a sufficient second-order condition for a weak local minimum in a simple optimal control problem with one control constraint G(u) ≤ 0, given by a C2-function. A similar second-order condition was obtained earlier by the author for a strong minimum in a much more general problem. In the present paper, we would like to take a narrower perspective than before and thus provide shorter and simpler proofs. In addition, the paper uses the first and second order tangents to the set U, defined by the inequality G(u) ≤ 0. The main difficulty of the proof, clearly shown in the paper, refers to the set, where the gradient Hu of the Hamiltonian is small, but the condition of quadratic growth of the Hamiltonian is satisfied. The paper can be valuable for self-explanation and provides a basis for extensions.
    Źródło:
    Control and Cybernetics; 2022, 51, 2; 151--169
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    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:
    Second-order sufficient conditions for an extremum in optimal control
    Autorzy:
    Osmolovskij, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/206727.pdf
    Data publikacji:
    2002
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    ekstremala łamana
    forma kwadratowa
    minimum silne
    minimum słabe
    stożek krytyczny
    warunek dostatecznej optymalności
    zasada maksimum
    accessory problem
    broken extremal
    control discontinuities
    critical cone
    maximum principle
    quadratic form
    strong minimum
    suffcient optimality condition
    weak minimum
    Opis:
    Suffcient quadratic optimality conditions for a weak and a strong minimum are stated in an optimal control problem on a fixed time interval with mixed state-control constraints, under the assumption that the gradients of all active mixed constraints with respect to control are linearly independent. The conditions are stated for the cases of both continuous and discontinuous controls and guarantee in each case a lower bound of the cost function increase at t1e reference point. They are formulated in terms of an accessory problem with quadratic form, which must be positive-definite on the so-called critical cone. In the case of discontinuous control the quadratic form has some new terms related to the control discontinuity.
    Źródło:
    Control and Cybernetics; 2002, 31, 3; 803-831
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-15 z 15

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