Open AccessBook
Optimization and nonsmooth analysis
TLDR
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
Citations
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A geometrical approach to monotone functions in R n
Giovanni Alberti,Luigi Ambrosio +1 more
TL;DR: In this paper, the fine properties of monotone functions on Ω(n)-convex convex functions were studied. Butler et al. studied the continuity and differentiability properties of these functions, the approximability properties, the structure of the distributional derivatives and the weak Jacobians.
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A new technique for inconsistent QP problems in the SQP method
TL;DR: Numerical results are reported which show that this technique for regularizing inconsistent QP problems, combined with a special method for the case of regular subproblems, is quite competitive to highly appreciated established ones.
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A SEIR model for control of infectious diseases with constraints
TL;DR: This paper proposes the introduction of constraints involving state variables on an optimal control problem applied to a compartmental SEIR (Susceptible. Exposed, Infectious and Recovered) model to study the solution of problems when mixed state control constraints are used to impose upper bounds on the available vaccines.
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An Infeasible Primal-Dual Algorithm for Total Bounded Variation--Based Inf-Convolution-Type Image Restoration
TL;DR: The globalized primal-dual algorithm introduced in this paper works with generalized derivatives, converges locally at a superlinear rate, and is stable with respect to noise in the data.