Sublevel sets of invex functions are connected under mild assumptions, with the result extended to solution sets in invex-incave minimax problems and incave games.
Invex programs: First order algorithms and their convergence, 2023
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On the Connectedness of Sublevel Sets in Invex Optimization
Sublevel sets of invex functions are connected under mild assumptions, with the result extended to solution sets in invex-incave minimax problems and incave games.