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Optimization and nonsmooth analysis
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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
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Stability results for Ekeland's e-variational principle and cone extremal solutions
Hedy Attouch,Hassan Riahi +1 more
TL;DR: The Ekeland's e-variational principle asserts the existence of a point xI in X, which is called e-extremal with respect to f, which satisfies the semi continuity properties of the mapping which to f associates e- Ext f the set of such e-Extremal points.
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On parametric nonlinear programming
TL;DR: In this paper, a tutorial survey of finite dimensional optimization problems which depend on parameters is presented, focusing on unfolding and singularity theory, structural analysis of families of constraint sets, constrained optimization problems and semi-infinite optimization.
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An augmented Lagrangian dual approach for the H-weighted nearest correlation matrix problem
Houduo Qi,Defeng Sun +1 more
TL;DR: An augmented Lagrangian dual-based approach that avoids the explicit computation of the metric projection under the H-weight and solves a sequence of unconstrained convex optimization problems, each of which can be efficiently solved by an inexact semismooth Newton method combined with the conjugate gradient method.
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Second-order discrete approximation to linear differential inclusions
TL;DR: In this paper, an approximation to a linear differential inclusion by means of N-stage single step discrete inclusions is presented, which is of second-order accuracy with respect to N. Approximations of this type with higher order of accuracy are shown not to exist, in general.
Optimization Algorithms on Riemannian Manifolds with Applications
TL;DR: In this paper, the authors generalized three well-known unconstrained optimization approaches for Rn to solve optimization problems with constraints that can be viewed as a d-dimensional Riemannian manifold.