Geodesic
A moving asymptotes algorithm using new local convex approximation methods with explicit solutions
Electronic transactions on numerical analysis, Tome 43 (2015).

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Summary: In this paper we propose new local convex approximations for solving unconstrained non-linear optimization problems based on a moving asymptotes algorithm. This method incorporates second-order information for the moving asymptotes location. As a consequence, at each step of the iterative process, a strictly convex approximation subproblem is generated and solved. All subproblems have explicit global optima. This considerably reduces the computational cost of our optimization method and generates an iteration sequence. For this method, we prove convergence of the optimization algorithm under basic assumptions. In addition, we present an industrial problem to illustrate a practical application and a numerical test of our method.
Classification : 65K05, 65K10, 65L10, 90C30, 46N10
Keywords: geometric convergence, nonlinear programming, method of moving asymptotes, multivariate convex approximation 
@article{ETNA_2015__43__a10,
     author = {Bachar, Mostafa and Estebenet, Thierry and Guessab, Allal},
     title = {A moving asymptotes algorithm using new local convex approximation methods with explicit solutions},
     journal = {Electronic transactions on numerical analysis},
     publisher = {mathdoc},
     volume = {43},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2015__43__a10/}
}
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Bachar, Mostafa; Estebenet, Thierry; Guessab, Allal. A moving asymptotes algorithm using new local convex approximation methods with explicit solutions. Electronic transactions on numerical analysis, Tome 43 (2015). http://geodesic.mathdoc.fr/item/ETNA_2015__43__a10/