Geodesic
Modified Projected Newton Scheme for Non-Convex Function With Simple Constraints
Yugoslav journal of operations research, Tome 31 (2021) no. 3, p. 319

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In this paper, a descent line search scheme is proposed to find a local minimum point of a non-convex optimization problem with simple constraints. The idea ensures that the scheme escapes the saddle points and finally settles for a local minimum point of the non-convex optimization problem. A positive definite scaling matrix for the proposed scheme is formed through symmetric indefinite matrix factorization of the Hessian matrix of the objective function at each iteration. A numerical illustration is provided, and the global convergence of the scheme is also justified.
Classification : 90C26, 90C30
Keywords: Projected Newton Scheme, Non-convex Function, Simple Constraints, Saddle Point, Local Minimum Point 
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     title = {Modified {Projected} {Newton} {Scheme} for {Non-Convex} {Function} {With} {Simple} {Constraints}},
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Suvra Kanti Chakraborty; Geetanjali Panda. Modified Projected Newton Scheme for Non-Convex Function With Simple Constraints. Yugoslav journal of operations research, Tome 31 (2021) no. 3, p. 319 . http://geodesic.mathdoc.fr/item/YJOR_2021_31_3_a2/