#### Le Thanh Tung, Dang Hoang Tam, Homeomorphic optimality conditions and duality for semi-infinite programming on smooth manifolds, Vol. 2021 (2021), Article ID 18, pp. 1-18

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DOI: 10.23952/jnfa.2021.18

Received December 12, 2020; Accepted April 28, 2021; Published May 26, 2021

Abstract. In this paper, we explore the semi-infinite programming on smooth manifolds. We first discuss the optimality conditions for semi-infinite programming on smooth manifolds via homeomorphic optimality conditions for the associated problems. Further, we present Lagrange, Mond-Weir, and Wolfe type duality for the semi-infinite programming on manifolds, and examine weak and strong duality relations under the $\varphi^{-1}$-convexity assumption.