The local Lipschitz continuity condition is standard in nonsmooth, nonconvex optimization -- see e.g. this paper and Sections "Nonsmooth, Nonconvex Optimization" and "The Clarke Subdifferential" in these lecture notes. The Lipschitz continuity condition is also used in stochastic convex optimization problems -- see e.g. this paper.

The Lipschitz continuity condition plays important roles in isoperimetric inequalities and optimal mass transportation theory.

The local Lipschitz continuity condition is standard in nonsmooth, nonconvex optimization -- see e.g. this paper and Sections "Nonsmooth, Nonconvex Optimization" and "The Clarke Subdifferential" in these lecture notes.

The Lipschitz continuity condition is also used in stochastic convex optimization problems -- see e.g. this paper.

The Lipschitz continuity condition plays important roles in stochastic differential equations, isoperimetric inequalities, and optimal mass transportation theory.

The local Lipschitz continuity condition is standard in nonsmooth, nonconvex optimization -- see e.g. this paper and Sections "Nonsmooth, Nonconvex Optimization" and "The Clarke Subdifferential" in these lecture notes.

The local Lipschitz continuity condition is standard in nonsmooth, nonconvex optimization -- see e.g. this paper and Sections "Nonsmooth, Nonconvex Optimization" and "The Clarke Subdifferential" in these lecture notes. The Lipschitz continuity condition is also used in stochastic convex optimization problems -- see e.g. this paper.

The Lipschitz continuity condition plays important roles in isoperimetric inequalities and optimal mass transportation theory.