Temat: second-order optimality

Skocz do pozycji: 1.

Tytuł:: On relations among the generalized second-order directional derivatives
Autorzy:: Pastor, Karel
Tematy:: generalized second-order directional derivative
convexity
second-order optimality conditions; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/729322.pdf Link otwiera się w nowym oknie
Opis:: In the paper, we deal with the relations among several generalized second-order directional derivatives. The results partially solve the problem which of the second-order optimality conditions is more useful.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Second-order optimality conditions in nonsmooth vector optimization
Autorzy:: Yadav, Priyanka
Tematy:: vector optimization
cones
nonsmooth second-order cone-convexity
second-order optimality
duality; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/31342762.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Revisiting the analysis of optimal control problems with several state constraints
Autorzy:: Bonnans, J. F.
Hermant, A.
Tematy:: optimal control
state constraints
shooting algorithm
second order optimality conditions; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/970908.pdf Link otwiera się w nowym oknie
Opis:: This paper improves the results of and gives shorter proofs for the analysis of state constrained optimal control problems than presented by the authors in Bonnans and Hermant (2009b), concerning second order optimality conditions and the well-posedness of the shooting algorithm. The hypothesis for the second order necessary conditions is weaker, and the main results are obtained without reduction to the normal form used in that reference, and without analysis of high order regularity results for the control. In addition, we provide some numerical illustration. The essential tool is the use of the "alternative optimality system".
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Sensitivity analysis for optimal control of problems governed by semilinear parabolic equations
Autorzy:: Bergounioux, M.
Merabet, N.
Tematy:: analiza czułości
sterowanie optymalne
optimal control
second order optimality conditions
sensitivity analysis; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/206854.pdf Link otwiera się w nowym oknie
Opis:: We investigate an optimal control problem governed by a semilinear parabolic equation with perturbed initial data. We perform some sensitivity analysis: under polyhedricity assumption and second order optimality conditions we derive second order expansion of the optimal value function.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Second order convexity and a modified objective function method in mathematical programming
Autorzy:: Antczak, T.
Tematy:: programowanie matematyczne
mathematical programming
second order modified objective function optimization problem
second order convex function
second order optimality conditions; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/969778.pdf Link otwiera się w nowym oknie
Opis:: An approach to nonlinear constrained mathematical programming problems which makes use of a second order derivative is presented. By using a second order modified objective function method, a modified optimization problem associated with a primal mathematical programming problem is constructed. This auxiliary optimization problem involves a second order approximation of an objective function constituting the primal mathematical programming problem. The equivalence between the original mathematical programming problem and its associated modified optimization problem is established under second order convexity assumption. Several practical O.R. applications show that our method is efficient. Further, an iterative algorithm based on this approach for solving the considered nonlinear mathematical programming problem is given for the case when the functions constituting the problem are second order convex. The convergence theorems for the presented algorithm are established.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 6.

Tytuł:: Optimality conditions for a class of optimal boundary control problems with quasilinear elliptic equations
Autorzy:: Casas, E.
Dhamo, V.
Tematy:: optimal control
Neumann boundary control
quasi-linear elliptic equation
Pontryagin principle
second order optimality conditions; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/206408.pdf Link otwiera się w nowym oknie
Opis:: First- and second-order optimality conditions are established for the boundary optimal control of quasilinear elliptic equations with pointwise constraints on the control. The theory is developed for Neumann controls in polygonal domains of dimension two. For the derivation of second-order sufficient optimality conditions, which is the main goal of this paper, the regularity of the solutions to the state equation and its linearization is studied in detail. Moreover, a Pontryagin principle is proved. The main difficulty in the analysis of these problems is the nonmonotone character of the state equation.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: Exact penalization of pointwise constraints for optimal control problems
Autorzy:: Casas, E.
Tematy:: optimal control
semilinear elliptic equations
pointwise state constraints
exact penalization
first and second order optimality conditions; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/970884.pdf Link otwiera się w nowym oknie
Opis:: In this paper we consider a control problem governed by a semilinear elliptic equation with pointwise control and state constraints. We analyze the existence of an exact penalization of the state constraints. In particular, we prove that the first and second order optimality conditions imply the existence of such a penalization. Finally, we prove some extra regularity of the strict local minima of the control problem, assuming the existence of an exact penalization for them.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 8.

Tytuł:: Lipschitz stability of optimal controls for the steady-state Navier-Stokes equations
Autorzy:: Roubicek, T.
Troltzsch, F.
Tematy:: sterowanie strumieniem danych
stabilność Lipschitza
incompressible viscous fluids
flow control
first and second order optimality conditions
Lipschitz stability; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/970527.pdf Link otwiera się w nowym oknie
Opis:: An optimal control problem with quadratic cost functional for the steady-state Navier-Stokes equations with no-slip boundary condition is considered. Lipschitz stability of locally optimal controls with respect to certain perturbations of both the cost functional and the equation is proved provided a second-order sufficient optimality condition holds. For a sufficiently small Reynolds number, even global Lipschitz stability of the unique optimal control is shown.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 9.

Tytuł:: C^11 vector optimization problems and Riemann derivatives
Autorzy:: Ginchev, I.
Guerraggio, A.
Rocca, M.
Tematy:: optymalizacja wektorowa
pochodna kierunkowa typu Riemanna
warunek optymalności dwuwskaźnikowy
vector optimization
Riemann-type directional derivatives
second-order optimality conditions; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/970359.pdf Link otwiera się w nowym oknie
Opis:: In this paper we introduce a generalized second-order Riemann-type derivative for C^1'1 vector functions and use it to establish necessary and sufficient optimality conditions for vector optimization problems. We show that, these conditions are stronger than those obtained by means of the second-order subdinerential in Clarke sense considered in Guerraggio, Luc (2001) and also to some extent than those obtained in Guerraggio, Luc, Minh (2001).
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 10.

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.
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; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/2183496.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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