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Shanjian Tang. A second-order maximum principle for singular optimal stochastic controls. Global impulsive optimal control computation. A nonsmooth maximum principle for optimal control problems with state and mixed constraints - convex case.

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Conference Publications , , Special : Hans Josef Pesch. Michael Basin , Pablo Rodriguez-Ramirez. An optimal impulsive control regulator for linear systems. The maximum principle for linear infinite dimensional control systems with state constraints. Shaolin Ji , Xiaole Xue. A stochastic maximum principle for linear quadratic problem with nonconvex control domain. Guirong Jiang , Qishao Lu. The dynamics of a Prey-Predator model with impulsive state feedback control. State feedback impulsive control of computer worm and virus with saturated incidence.

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A neighboring extremal solution for an optimal switched impulsive control problem. Distributed optimal control of a nonstandard nonlocal phase field system with double obstacle potential. Hancheng Guo , Jie Xiong. A second-order stochastic maximum principle for generalized mean-field singular control problem.

Value function for regional control problems via dynamic programming and Pontryagin maximum principle. Qizhen Xiao , Binxiang Dai. Heteroclinic bifurcation for a general predator-prey model with Allee effect and state feedback impulsive control strategy. Matthias Gerdts , Martin Kunkel. Convergence analysis of Euler discretization of control-state constrained optimal control problems with controls of bounded variation. Optimal control of piecewise affine systems with piecewise affine state feedback.

Fulvia Confortola , Elisa Mastrogiacomo. Feedback optimal control for stochastic Volterra equations with completely monotone kernels.

Yunfei Peng , X. A class of nonlinear impulsive differential equation and optimal controls on time scales. Nonlinear state-dependent impulsive system in fed-batch culture and its optimal control. American Institute of Mathematical Sciences. Previous Article Global optimization reduction of generalized Malfatti's problem. Sufficient optimality conditions for extremal controls based on functional increment formulas. Evans , Quasiconvexity and partial regularity in the calculus of variations.

Evans and R. Gariepy , Blowup, compactness and partial regularity in the calculus of variations. Indiana Univ. Fonseca and G. Francfort , 3 D - 2 D asymptotic analysis of an optimal design problem for thin films. Reine Angew. Fonseca and N. Fusco , Regularity results for anisotropic image segmentation models.

Scuola Norm. Pisa Cl. Numdam MR Zbl Leoni , Bulk and contact energies: Nucleation and relaxation. SIAM J.

## Bibliografie | Institute of Information Theory and Automation

Friesecke , A necessary and sufficient condition for non attainment and formation of microstructure almost everywhere in scalar variational problems. Royal Soc. Marcellini , A relation between existence of minima for nonconvex integrals and uniqueness for not strictly convex integrals of the calculus of variations , Math. Theories of Optimization, edited by J. Cecconi and T. Springer-Verlag, Lecture Notes in Math. Mascolo and R. Schianchi , Existence theorems for nonconvex problems.

Pures Appl. Schianchi , Nonconvex problems in the calculus of variations. MR Schianchi , Existence theorems in the calculus of variations. We remark that relations 1 and 2 and the last relation in 3 hold true also for an efficient solution.

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We shall introduce a definition of univexity of the above functional, which will be useful to state the results established in the paper. Definition 3. Example 3. We get. In order to prove this result, we use the concept of univexity defined above for a vectorial functional. Theorem 3.

Further , assume that the following hypotheses are fulfilled :. We obtain. If we impose some stronger assumption on the objective function, then we can prove a stronger result. Hence, the proof of the theorem is complete. Proposition 4. Theorem 4. Suppose that the following hypotheses are satisfied :. Suppose, contrary to the result, that the inequality. Proposition 5. Further , assume that the following hypotheses are satisfied :. In this research paper, a new class of nonconvex multitime variational problems has been considered. We have defined the concept of univexity for a path-independent curvilinear vector functional as a generalization of a vector-valued univex function.

The so-called univex functions unify many various classes of generalized convex concepts in optimization theory. Therefore, the sufficient optimality conditions for proper efficiency and several duality theorems in the sense of Mond-Weir and in the sense of Wolfe, which have been established in the paper, for a new class of nonconvex multitime multiobjective variational problems extend adequate results already existing in optimization theory.

## Nonconvex Optimal Control and Variational Problems

Aghezzaf B, Khazafi K: Sufficient conditions and duality for multiobjective variational problems with generalized B -invexity. Control Cybern. Nonlinear Anal.