Geodesic
Penalty method with descent for problems of convex optiization
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2019), pp. 48-64

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We propose a penalty method for general convex constrained optimization problems, where each auxiliary penalized problem is replaced with an equivalent mixed variational inequality problem. This allows one to keep the decomposable structure of the initial problem and to simplify the direction finding subproblem. A gap function is utilized for evaluation of solution accuracy of the auxiliary penalized problem. Convergence of the method in primal and dual variables is established under rather weak assumptions.
Keywords: convex optimization problem, non-linear constraints, penalty method, descent method
Mots-clés : decomposition. 
@article{IVM_2019_7_a4,
     author = {I. V. Konnov},
     title = {Penalty method with descent for problems of convex optiization},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {48--64},
     publisher = {mathdoc},
     number = {7},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_7_a4/}
}
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%F IVM_2019_7_a4
I. V. Konnov. Penalty method with descent for problems of convex optiization. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2019), pp. 48-64. http://geodesic.mathdoc.fr/item/IVM_2019_7_a4/