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Optimization and nonsmooth analysis
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The Calculus of Variations as discussed by the authors is a generalization of the calculus of variations, which is used in many aspects of analysis, such as generalized gradient descent and optimal control.Abstract:
1. Introduction and Preview 2. Generalized Gradients 3. Differential Inclusions 4. The Calculus of Variations 5. Optimal Control 6. Mathematical Programming 7. Topics in Analysis.read more
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An Extension of the Second Welfare Theorem to Economies with Nonconvexities and Public Goods
M. Ali Khan,Rajiv Vohra +1 more
TL;DR: In this paper, a generalization of the results of Foley and Guesnerie on the second welfare theorem to economies with arbitrary nonconvex production sets is reported, and the nature of marginal cost prices in such economies is clarified through the use of the Clarke tangent cones.
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Models and a relaxation algorithm for continuous network design problem with a tradable credit scheme and equity constraints
TL;DR: This paper model CNDP which has a tradable credit scheme and equity constraints in order to research on the way of releasing congestion by combining increasing supply and reducing demand.
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Distributed Frequency Control With Operational Constraints, Part I: Per-Node Power Balance
TL;DR: This paper addresses the distributed optimal frequency control of multi-area power system with operational constraints, including the regulation capacity of individual control area and the power limits on tie-lines, and studies two control modes: the per-node balance mode and the network balance mode.
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Finite-Time Consensus on the Median Value With Robustness Properties
TL;DR: It is proved that despite the persistent influence of (at most) a certain number of uncooperative agents, the cooperative agents achieve finite time consensus on a value lying inside the convex hull of the Cooperative agents' initial conditions, provided that the special class of so-called “$k$-safe” network topology is considered.
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Optimality conditions for non-finite valued convex composite functions
James V. Burke,R. A. Poliquin +1 more
TL;DR: A technique for reducing the infinite valued case to the finite valued one is presented and this technique is extended to extend the results in Burke (1987) to the case in which the convex function may take infinite values.