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
Ben-Tal, Second-order and related extremality conditions in nonlinear program- ming,Journal of Optimization Theory and Applications31(1980), 143–165
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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