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1

Variational analysis of one-dimensional nonconvex Neumann problem

Puchała P.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2011

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Vol. 10, nr 1

215-221

EN

We consider a variational formulation of a nonconvex one-dimensional Neumann problem. The method of obtaining infimum of a relevant functional is based on a general theorem attributed to Z. Naniewicz, of the minimization of a certain class of nonconvex functionals.

2

Zastosowanie analizy wariantowej do tworzenia konstrukcji wzorcowej

Chyra P., Gendarz P.

Górnictwo Odkrywkowe

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2008

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R. 49/2, nr 4-5

190-197

PL

Praca poświęcona jest analizie narzędzi weryfikacji wytrzymałościowej MES z punktu widzenia ich przydatności do tworzenia konstrukcji wzorcowych wymaganych w procesach tworzenia typoszeregów konstrukcji metodą podobieństwa konstrukcyjnego. Praca obejmuje swym zakresem analizy modułu OPTIMIZATION z aplikacji SIMULATION zaawansowanego programu graficznego I-DEAS.

EN

The paper treats about strength of materials verification with use of finished elements method (FEM) as a support of creating the ordered construction families method. Analyzed OPTIMIZATION task of the SIMULATION application from I-DEAS software enable optimization solutions of constructional quantity type features with mass, stress and displacement criterions. The main goal of taken studies is to exam presented software tools as useful for finding basic construction of creating the ordered construction families by construction similarity method.

3

Optimal control of delay-differential inclusions with multivalued initial conditions in infinite dimensions

Mordukhovich B. S., Wang D., Wang L.

Control and Cybernetics

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2008

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Vol. 37, no 2

393-428

EN

This paper is devoted to the study of a general class of optimal control problems described by delay-differential inclusions with infinite-dimensional state spaces, endpoints constraints, and multivalued initial conditions. To the best of our knowledge, problems of this type have not been considered in the literature, except for some particular cases when either the state space is finite-dimensional or there is no delay in the dynamics. We develop the method of discrete approximations to derive necessary optimality conditions in the extended Euler-Lagrange form by using advanced tools of variational analysis and generalized differentiation in infinite dimensions. This method consists of the three major parts: (a) constructing a well-posed sequence of discrete-time problems that approximate in an appropriate sense the original continuous-time problem of dynamic optimization; (b) deriving necessary optimality conditions for the approximating discrete-time problems by reducing them to infinite-dimensional problems of mathematical programming and employing then generalized differential calculus; (c) passing finally to the limit in the obtained results for discrete approximations to establish necessary conditions for the given optimal solutions to the original problem. This method is fully realized in the delay-differential systems under consideration.

4

Slope stability analysis by variational method with genetic algorithm application. Part 2: Genetic algorithm with advanced techniques. Simple modeling of uncertainties

Srokosz P. E.

Archives of Civil Engineering

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2007

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Vol. 53, nr 2

269-292

EN

In the paper the genetic algorithm with advanced techniques is presented in details. The possibility of direct application of the proposed genetic algorithm's improvements in the slope stability evaluation is discussed. The problem of the uncertainties in geotechnical data and numerical implementations of the algorithms with their influences on the stability calculations is touched. The simple method of modeling of the uncertainties in the calculation data is proposed also. All the newest versions of the procedures were tested on the same example of slope, as presented in the Part 1 of the paper.

PL

Przedstawiono szczegółowo algorytm genetyczny z technikami zaawansowanymi. Omówiono możliwość bezpośredniego zastosowania proponowanych ulepszeń w algorytmie genetycznym w ocenie stateczności zboczy. Poruszono problem niepewności danych geotechnicznych i numerycznych implementacji algorytmów oraz ich wpływ na obliczenia stateczności. Zaproponowano także prostą metodę modelowania niepewności danych obliczeniowych. Wszystkie najnowsze wersje procedur zostały przetestowane na przykładzie zbocza z Części 1-szej artykułu.

5

Optimal control of semilinear evolution inclusions via discrete approximations

Mordukhovich B. S., Wang D.

Control and Cybernetics

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2005

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Vol. 34, no 3

849-870

EN

This paper studies a Mayer type optimal control problem with general endpoint constraints for semilinear unbounded evolution inclusions in reflexive and separable Banach spaces. First, we construct a sequence of discrete approximations to the original optimal control problem for evolution inclusions and prove that optimal solutions to discrete approximation problems uniformly converge to a given optimal solution for the original continuous-time problem. Then, based on advanced tools of generalized differentiation, we derive necessary optimality conditions for discrete-time problems under fairly general assumptions. Combining these results with recent achievements of variational analysis in infinite-dimensional spaces, we establish new necessary optimality conditions for constrained continuous-time evolution inclusions by passing to the limit from discrete approximations.

6

Optimal control of constrained delay-differential inclusions with multivalued initial conditions

Mordukhovich B. S., Wang L.

Control and Cybernetics

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2003

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Vol. 32, no 3

585-609

EN

This paper studies a general optimal control problem for nonconvex delay-differential inclusions with endpoint constraints. In contrast to previous publications on this topic, we incorporate time-dependent set constraints on the initial interval, which are specific for systems with delays and provide an additional source for optimization. Our variational analysis is based on well-posed discrete approximations of constrained delay-differential inclusions by a family of time-delayed systems with discrete dynamics and perturbed constraints. Using convergence results for discrete approximations and advanced tools of nonsmooth variational analysis, we derive necessary optimality conditions for constrained delay-differential inclusions in both Euler-Lagrange and Hamiltonian forms involving nonconvex generalized differential constructions for nonsmooth functions, sets, and set-valued mappings.

7

Mixed coderivatives of set-valued mappings in variational analysis

Mordukhovich B. S., Shao Y.

Journal of Applied Analysis

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1998

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Vol. 4, nr 2

269-294

EN

We consider a refined coderivative construction for nonsmooth and set-valued mappings between Banach spaces. This limiting mixed coderivative is different from "normal" coderiva-tives generated by normal cones/subdifferentials and turns out to be useful for studying some basic propertiers in variational analysis particularly related to Lipschitzian stability. We develop a strong calculus for this coderivative important for various applications.