In this article, we have introduced the concept of \textit{geodesic -invex set} and by using this concept the notion of \textit{geodesic -preinvex functions} and \textit{geodesic -invex functions} are developed on a Riemannian manifold. Moreover, several properties and results are deduced within af…
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5 results for “Invexity”
Defines new types of preinvex functions for optimization.
problem Optimization problems with new types of preinvex functions.
method Definition and analysis of w-invex functions.
result New types of preinvex functions solve optimization problems.
Sparse Mixed Linear Regression with Guarantees: Taming an Intractable Problem with Invex Relaxationcs.LG
Paper solves NP-hard sparse mixed linear regression problem with provable guarantees.
problem Sparse mixed linear regression on unlabeled data.
method Invex relaxation for intractable problem with theoretical guarantees.
result Exact recovery of data labels and close approximation of regression parameters.
The paper defines new geometric concepts on Riemannian manifolds and applies them to optimization problems.
problem Optimization problems on Riemannian manifolds.
method Strongly geodesic preinvexity, strongly η-invexity, and strongly invariant η-monotonicity definitions.
result Characterization of strict η-minimizers and solutions to variational like-inequality problems.
Paper analyzes convergence rates of SGD for non-convex functions under various assumptions.
problem Analyzing convergence rates of SGD for non-convex functions.
method Studied convergence properties of Stochastic Gradient Descent (SGD) for invex functions under weaker and stronger hypotheses.
result Derives estimates on the rate of convergence of $J(oldsymbolθ_t)$ to its limit for functions satisfying the Polyak-Lojasiewicz (PL) condition.