We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.
Nonholonomic systems with inequality constraints
Explicit formulas for projections onto intersection of a finite number of halfspaces
Subgradient methods with variants of Polyak stpsize for quasi-convex optimization with inequality constraints for analogues of sharp minima
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