Nonsmooth extension of the Brezzi-Rappaz-Raviart approximation theorem via metric regularity, applied to quasi-optimal finite-element error estimates for viscous Hamilton-Jacobi equations and second-order mean field games.
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Derives first- and second-order necessary and sufficient optimality conditions for directional local minimality in unconstrained nonsmooth optimization and adapts them to nondirectional local minimality using critical directions.
Derives second-order Dini formulas for efficient solution maps S from marginal maps Φ under value-to-decision error bounds and metric regularity conditions in parametric vector optimization.
Under directional rank stability and semialgebraic parabolic arc-realizability, outer, inner, and arc-generated parabolic tangent sets of basic closed semialgebraic sets coincide with algebraic second-order linearized sets, yielding checkable second-order necessary and sufficient conditions for quad
Approximate directional stationarity is formulated as a necessary optimality condition for nonsmooth constrained problems, with a qualification condition using one sequence to infer directional stationarity.
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A nonsmooth extension of the Brezzi-Rappaz-Raviart approximation theorem via metric regularity techniques and applications to nonlinear PDEs
Nonsmooth extension of the Brezzi-Rappaz-Raviart approximation theorem via metric regularity, applied to quasi-optimal finite-element error estimates for viscous Hamilton-Jacobi equations and second-order mean field games.
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On directional local minimality and directional optimality conditions in nonsmooth optimization
Derives first- and second-order necessary and sufficient optimality conditions for directional local minimality in unconstrained nonsmooth optimization and adapts them to nondirectional local minimality using critical directions.
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Second-Order Sensitivity of Efficient Solution and Marginal Maps in Parametric Vector Optimization with Set Constraints
Derives second-order Dini formulas for efficient solution maps S from marginal maps Φ under value-to-decision error bounds and metric regularity conditions in parametric vector optimization.
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Parabolic second-order tangent sets of semialgebraic sets and applications to polynomial optimization
Under directional rank stability and semialgebraic parabolic arc-realizability, outer, inner, and arc-generated parabolic tangent sets of basic closed semialgebraic sets coincide with algebraic second-order linearized sets, yielding checkable second-order necessary and sufficient conditions for quad
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Approximate directional stationarity and associated qualification conditions
Approximate directional stationarity is formulated as a necessary optimality condition for nonsmooth constrained problems, with a qualification condition using one sequence to infer directional stationarity.