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《Optimization》2012,61(4):509-529
This article studies multiobjective optimal control problems in the discrete time framework and in the infinite horizon case. The functions appearing in the problems satisfy smoothness conditions. This article generalizes to the multiobjective case results obtained for single-objective optimal control problems in that framework. The dynamics are governed by difference equations or difference inequations. Necessary conditions of Pareto optimality are presented, namely Pontryagin maximum principles in the weak form and in the strong form. Sufficient conditions are also provided. Other notions of Pareto optimality are defined when the infinite series do not necessarily converge. 相似文献
144.
《Optimization》2012,61(8):1247-1258
In this article, the standard primal and dual linear semi-infinite programming (DLSIP) problems are reformulated as linear programming (LP) problems over cones. Therefore, the dual formulation via the minimal cone approach, which results in zero duality gap for the primal–dual pair for LP problems over cones, can be applied to linear semi-infinite programming (LSIP) problems. Results on the geometry of the set of the feasible solutions for the primal LSIP problem and the optimality criteria for the DLSIP problem are also discussed. 相似文献
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《Optimization》2012,61(6):1245-1260
ABSTRACTIn this paper, we derive some optimality and stationarity conditions for a multiobjective problem with equilibrium constraints (MOPEC). In particular, under a generalized Guignard constraint qualification, we show that any locally Pareto optimal solution of MOPEC must satisfy the strong Pareto Kuhn-Tucker optimality conditions. We also prove that the generalized Guignard constraint qualification is the weakest constraint qualification for the strong Pareto Kuhn-Tucker optimality. Furthermore, under certain convexity or generalized convexity assumptions, we show that the strong Pareto Kuhn-Tucker optimality conditions are also sufficient for several popular locally Pareto-type optimality conditions for MOPEC. 相似文献
148.
《Optimization》2012,61(6):861-873
An optimal control problem governed by a variational inequality of elliptic type is considered. Necessary optimality conditions are obtained and, in some special cases, the optimal control is determined. 相似文献
149.
Recent results by Eberhard et al. (2006) [4] and Eberhard and Wenczel (2009) [3] on the interaction of single- and double-envelope operations of nonsmooth functions and their interaction with second-order derivations have been used to study tilt-stability of local minima. This continues the study begun by Poliquin and Rockafellar (1998) [1] but now, armed with new tools we are able to make some new observations. We observe that tilt-stability entails a local density within the graph of the proximal subderivative of strict local minima order two of the tilted function. Indeed, it also entails the strict local minimality (order two) of the tilt-stable local minimum itself. For prox-regular, subdifferentially continuous functions this density property characterises tilt stability. 相似文献
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