A set-valued gap function, $$\phi $$ ϕ , existing in the literature for smooth and nonsmooth multiobjective optimization problems is dealt with. It is known that $$0\in \phi (x^*)$$ 0 ∈ ϕ ( x ∗ ) is a sufficient condition for efficiency of a feasible solution $$x^*$$ x ∗ , while the converse does not hold. In the current work, the converse of this assertion is proved for properly efficient solutions. Afterwards, to avoid the complexities of set-valued maps some new single-valued gap functions, for nonsmooth multiobjective optimization problems with locally Lipschitz data are introduced. Important properties of the new gap functions are established.
Optimization Letters – Springer Journals
Published: Feb 2, 2017
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