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1
Content available Existence, uniqueness and convergence of simultaneous distributed-boundary optimal control problems
100%
Gariboldi C. M. , Tarzia D. A.
Control and Cybernetics
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2015
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tom Vol. 44, no. 1
5--17
EN
We consider a steady-state heat conduction problem P for the Poisson equation with Mied Bondary conditions in a bounded multidimensional domain Ω. We also consider a family of problems Pα for the same Poisson equation with mixed boundary conditions, α > 0 being the heat transfer coefficient defined on a portion Γ1 of the boundary. We formulate simultaneous distributed and Neumann boundary optimal control problems on the internal energy g within Ω and the heat flux q, defined on the complementary portion Γ2 of the boundary of Ω for quadratic cost functional. Here, the control variable is the vector (g,q). We prove existence and uniqueness of the optimal control (g,q) for the system state of P, and (gα,qα) for the system state of Pα, for each α > 0, and we give the corresponding optimality conditions. We prove strong convergence, in suitable Sobolev spaces, of the vectorial optimal controls, system and adjoint states governed by the problems Pα to the corresponding vectorial optimal control, system and adjoint states governed by the problem P, when the parameter α goes to infinity. We also obtain estimations between the solutions of these vectorial optimal control problems and the solution of two scalar optimal control problems characterized by fixed g (with boundary optimal control q) and fixed q (with distributed optimal control g), respectively, for cases both of α > 0 and α = ∞.
2
Content available remote Some identification problems for an anchovy larva model with diffusion
100%
Anita S. , Boussouar A.
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1999
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tom Vol. 9, no. 1/2
7-24
EN
We study some identification problems for an anchovy larva model with diffusion. Existence of the optimal control for an abstract identification problem is demonstrated and necessary and sufficient optimality conditions are established. Applications for the anchovy larva model with diffusion are indicated. The uniqueness of the optimal control is discussed.
3
Content available remote Analysis of optimality conditions for some topology optimization problems in elasticity
100%
Trabucho L.
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nr 1
127-137
EN
The subject of topology optimization has undergone an enormous practical development since the appearance of the paper by Bendso e and Kikuchi (1988), where some ideas from homogenization theory were put into practice. Since then, several engineering applications as well as different approaches have been developed successfully. However, it is difficult to find in the literature some analytical examples that might be used as a test in order to assess the validity of the solutions obtained with different algorithms. As a matter of fact, one is often faced with numerical instabilities requiring a fine tuning of the algorithm for each specific case. In this work, we develop a family of analytical solutions for very simple topology optimization problems, in the framework of elasticity theory, including bending and extension of rods, torsion problems as well as plane stress and plane strain elasticity problems. All of these problems are formulated in a simplified theoretical framework. A key issue in this type of problems is to be able to evaluate the sensitivity of the homogenized elastic coefficients with respect to the microstructure parameter(s). Since we are looking for analytical solutions, we use laminates for which an explicit dependence of the homogenized coefficients on the microstructure is known.
4
A characterization of strict local minimizers of order one for static minmax problems in the parametric constraint case
88%
Taha A. W. A.
|
2000
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tom Vol. 6, nr 1
139-148
EN
We present a new version of first order necessary optimality conditions for a static minmax problem with inequality constraints in the parametric constraint case. These conditions, after some modification, turn out to characterize strict local minimizers of order one for the given problem.
5
Content available Continuous time non-smooth optimization through quasi efficiency
88%
Kumar P. , Sharma B.
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|
tom Vol. 52, No. 3
251--267
EN
The importance of quasi efficiency lies in its versatile nature as it permits a definite tolerable error that depend on the decision variables. This has been a motivating factor for us to introduce the notion of quasi efficient solution for the non-smooth multiobjective continuous time programming problem. Necessary optimality conditions are derived for this problem. To derive sufficient optimality conditions, the concept of approximate convexity has been extended to continuous case in this paper. A mixed dual is proposed for which weak and strong duality results are proved.
6
Content available Neumann boundary optimal control problems governed by parabolic variational equalities
88%
Bollo C. M. , Gariboldi C. M. , Tarzia D. A.
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tom Vol. 50, No. 2
227--252
EN
We consider a heat conduction problem S with mixed boundary conditions in an n-dimensional domain with regular boundary and a family of problems Sα with also mixed boundary conditions in , where α > 0 is the heat transfer coefficient on the portion of the boundary Г1. In relation to these state systems, we formulate Neumann boundary optimal control problems on the heat flux q which is definite on the complementary portion Г2 of the boundary of Ω. We obtain existence and uniqueness of the optimal controls, the first order optimality conditions in terms of the adjoint state and the convergence of the optimal controls, the system state and the adjoint state when the heat transfer coefficient α goes to infinity. Furthermore, we formulate particular boundary optimal control problems on a real parameter λ, in relation to the parabolic problems S and Sαα
7
Content available Necessary optimality conditions for robust nonsmooth multiobjective optimization problems
88%
Gadhi N. A. , Ohda M.
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2022
|
tom Vol. 51, No. 3
289--302
EN
This paper deals with a robust multiobjective optimization problem involving nonsmooth/nonconvex real-valued functions. Under an appropriate constraint qualification, we establish necessary optimality conditions for weakly robust efficient solutions of the considered problem. These optimality conditions are presented in terms of Karush-Kuhn-Tucker multipliers and convexificators of the related functions. Examples illustrating our findings are also given.
8
Content available Sufficient optimality criteria and duality for multiobjective variational control problems with B-(p,r)-invex function
88%
Antczak T. , Jimenez M. A.
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tom Vol. 34, no. 4
665--682
EN
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.
9
Content available remote Sufficient conditions of optimality for multiobjective optimization problems with γ-paraconvex data
75%
Amahroq T. , Taa A.
|
|
nr 3
239-247
EN
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.
10
Content available remote Optimality and sensitivity for semilinear bang-bang type optimal control problems
75%
Felgenhauer U.
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|
nr 4
447-454
EN
In optimal control problems with quadratic terminal cost functionals and systems dynamics linear with respect to control, the solution often has a bang-bang character. Our aim is to investigate structural solution stability when the problem data are subject to perturbations. Throughout the paper, we assume that the problem has a (possibly local) optimum such that the control is piecewise constant and almost everywhere takes extremal values. The points of discontinuity are the switching points. In particular, we will exclude the so-called singular control arcs, see Assumptions 1 and 2, Section 2. It is known from the results by Agrachev et al. (2002) stating that regularity assumptions, together with a certain strict second-order condition for the optimization problem formulated in switching points, are sufficient for strong local optimality of a state-control solution pair. This finite-dimensional problem is analyzed in Section 3 and optimality conditions are formulated (Lemma 2). Using well-known results concerning solution sensitivity for mathematical programs in R^n (Fiacco, 1983) one may further conclude that, under parameter changes in the problem data, the switching points will change Lipschitz continuously. The last section completes these qualitative statements by calculating sensitivity differentials (Theorem 2, Lemma 6). The method requires a simultaneous solution of certain linearized multipoint boundary value problems.
11
Content available remote Analysis of Optimality Conditions for Some Topology Optimization Problems in Elasticity
75%
Trabucho L.
|
|
tom Vol. 12, no 1
127-137
EN
The subject of topology optimization has undergone an enormous practical development since the appearance of the paper by Bends\o e and Kikuchi (1988), where some ideas from homogenization theory were put into practice. Since then, several engineering applications as well as different approaches have been developed successfully. However, it is difficult to find in the literature some analytical examples that might be used as a test in order to assess the validity of the solutions obtained with different algorithms. As a matter of fact, one is often faced with numerical instabilities requiring a fine tuning of the algorithm for each specific case. In this work, we develop a family of analytical solutions for very simple topology optimization problems, in the framework of elasticity theory, including bending and extension of rods, torsion problems as well as plane stress and plane strain elasticity problems. All of these problems are formulated in a simplified theoretical framework. A key issue in this type of problems is to be able to evaluate the sensitivity of the homogenized elastic coefficients with respect to the microstructure parameter(s). Since we are looking for analytical solutions, we use laminates for which an explicit dependence of the homogenized coefficients on the microstructure is known.
12
Content available Stable optimal design of two-dimensional elastic structures
75%
Cerkaev A. , Krog L. , Kucuk I.
Control and Cybernetics
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1998
|
tom Vol. 27, no 2
265-282
EN
We study optimal layout of piece-wise periodic structures of linearly elastic materials. The effective tensors of these structures are constant within pre-specified regions, the optimality is understood as the minimum of complementary energy. The suggested formulation leads to a construction that is stable under variation of the loading and which does not degenerates into checkerboard type structures. We derive necessary conditions of optimality of such layouts and analyse them. Numerically, we fins optimal structures for a number of examples, which are analyzed.
13
Second-order characterization of convex functions and its applications
63%
Nadi M. T. , Yao J. C. , Zafarani J.
|
|
tom Vol. 25, nr 1
49--58
EN
Some developments of the second-order characterizations of convex functions are investigated by using the coderivative of the subdifferential mapping. Furthermore, some applications of the second-order subdifferentials in optimization problems are studied.
14
On the multiobjective control problem
63%
Kumar P. , Sharma B.
|
|
tom Vol. 24, nr 2
223--231
EN
In this paper, sufficient optimality conditions are established for the multiobjective control problem using efficiency of higher order as a criterion for optimality. The ρ-type 1 invex functionals (taken in pair) of higher order are proposed for the continuous case. Existence of such functionals is confirmed by a numer of examples. It is shown with the help of an example that this class is more general than the existing class of functionals.Weak and strong duality theorems are also derived for a mixed dual in order to relate efficient solutions of higher order for primal and dual problems.
15
Content available Sterowanie optymalne systemami o parametrach rozłożonych z opóźnieniami
63%
Kowalewski A.
|
|
tom R. 15, nr 12
57-59
PL
W artykule dokonano przeglądu problematyki sterowania optymalnego systemami o parametrach rozłożonych z opóźnieniami w warunkach brzegowych. Zaprezentowano podstawowe zagadnienia dotyczące systemów o parametrach rozłożonych takie jak: istnienie i jednoznaczność rozwiązań, sterowanie optymalne rozłożone i brzegowe, sterowanie optymalne ze sprzężeniem zwrotnym, sterowanie czasowo-optymalne, sterowalność oraz modele matematyczne systemów o parametrach rozłożonych.
EN
In this article the review of optimal control problems for distributed parameter systems with boundary conditions involving time delays is performed. The principal problems, namely: existence and uniqueness of solutions, distributed and boundary optimal control, optimal feedback control, controllability and mathematical models of distributed parameter systems are presented.
16
Content available remote Optymalizacja pręta ściskanego przy warunkach stateczności dynamicznej
63%
Gajewski A.
|
|
tom Vol. 18
119--120
17
Content available Second-order conditions for boundary control problems of the Burgers equation
63%
Volkwein S.
Control and Cybernetics
|
2001
|
tom Vol. 30, no 3
249-278
EN
In this article control constrained optimal control problems for the Burgers equation are considered. First- and second-order optimality conditions are presented. Utilizing polyhedricity of the feasible set and the theory of Legendre-forms a second-order sufficient optimality condition is given that is very close to the second-order necessary optimality condition. For the numerical realization a prima-dual actrive set strategy is used.
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