Geodesic
Nonconvex optimization with nonlinear support functions
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 295-306

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We consider a special class of finite-dimensional optimization problems, in which the objective function and the constraint functions have convex support majorant functions and concave support minorant functions. For problems with inequality constraints, we propose and validate methods of successive convex optimization that converge to stationary solutions. For problems with equality constraints, we propose local search procedures with concave minorants.
Keywords: convex and concave support functions, local search, stationary point. 
@article{TIMM_2013_19_2_a28,
     author = {O. V. Khamisov},
     title = {Nonconvex optimization with nonlinear support functions},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {295--306},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a28/}
}
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O. V. Khamisov. Nonconvex optimization with nonlinear support functions. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 295-306. http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a28/