Preservation of Prox-Regularity of Sets with Applications to Constrained Optimization

DOI10.1137/15M1032739zbMath1333.49031MaRDI QIDQ2789607

Samir Adly, Florent Nacry, Lionel Thibault

Publication date: 2 March 2016

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

zbMATH Keywords

constrained optimizationmetric regularitysweeping processprox-regular functionssemiconvexityhypomonotonicityprox-regular sets

Mathematics Subject Classification ID

Nonlinear programming (90C30) Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53) Convexity of real functions of several variables, generalizations (26B25)

Related Items (26)

Unbounded second-order state-dependent Moreau's sweeping processes in Hilbert spaces ⋮ Explicit and implicit non-convex sweeping processes in the space of absolutely continuous functions ⋮ Optimal control of a nonconvex perturbed sweeping process ⋮ Existence of solutions for a Lipschitzian vibroimpact problem with time-dependent constraints ⋮ History-dependent operators and prox-regular sweeping processes ⋮ Lyapunov pairs for perturbed sweeping processes ⋮ Optimal control of nonconvex integro-differential sweeping processes ⋮ Prox-regularity approach to generalized equations and image projection ⋮ On the solution existence for prox-regular perturbed sweeping processes ⋮ Prox-regular sets and Legendre-Fenchel transform related to separation properties ⋮ Well-posedness of nonconvex degenerate sweeping process via unconstrained evolution problems ⋮ Distance function associated to a prox-regular set ⋮ A maximum principle for the controlled sweeping process ⋮ Convex and nonconvex sweeping processes with velocity constraints: well-posedness and insights ⋮ Direct proofs of intrinsic properties of prox-regular sets in Hilbert spaces ⋮ Subgradient projectors: extensions, theory, and characterizations ⋮ Unnamed Item ⋮ New metric properties for prox-regular sets ⋮ The contact problem in Lagrangian systems with redundant frictional bilateral and unilateral constraints and singular mass matrix. The all-sticking contacts problem ⋮ Nonsmooth dynamics of generalized Nash games ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Projected Dynamical Systems on Irregular, Non-Euclidean Domains for Nonlinear Optimization ⋮ Dynamical Systems Coupled with Monotone Set-Valued Operators: Formalisms, Applications, Well-Posedness, and Stability ⋮ Lyapunov stability of differential inclusions involving prox-regular sets via maximal monotone operators ⋮ Optimal Control of the Sweeping Process with a Nonsmooth Moving Set

Cites Work

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• Set-valued analysis

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