What is invexity?

By Adi Ben-Israel, B. Mond. 1986

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Euclidean Distance Geometry and Applications (2012, background): “dal function f(x) is a family of functions Fλ(x) such that F0(x) = f(x) for all x ∈RK and Fλ(x) has a decreasing number of local optima as λ increases. Eventually Fλ becomes convex, or at least invex [15], and its optimum xλ can be found using a single run of a local NLP solver. A homotopy continuat”
Learning Output Kernels with Block Coordinate Descent (2011, background): “Remarkably, invex functions can be characterized as follows (Craven & Glover, 1985; Ben-Israel & Mond, 1986).”
Invex sets and preinvex functions on Riemannian manifolds (2007, background): “Ben-Israel and Mond [5] introduced a new generalization of convex sets and convex functions and Craven [6] called them invex sets and preinvex functions, respectively.”
DINGO: Distributed Newton-Type Method for Gradient-Norm Optimization (2019, background): “When f is invex, [17, 18], the problems (1) and (4) have the same solutions.”
Efficient Output Kernel Learning for Multiple Tasks (2015, unknown): “. They could show that for the squared loss and V() = k k2 F the corresponding optimization problem is invex and directly optimize it. For an invex function every stationary point is globally optimal [22]. We follow a different path which leads to a formulation similar to the one of [2] used for lea”