TY - GEN
T1 - Approximation and optimization of polyhedral discrete and differential inclusions
AU - Mahmudov, Elimhan N.
PY - 2012
Y1 - 2012
N2 - In the first part of the paperoptimization of polyhedral discrete and differential inclusions is considered, the problem is reduced to convex minimization problem and the necessary and sufficient condition for optimality is derived. The optimality conditions for polyhedral differential inclusions based on discrete-approximation problem according to continuous problems are formulated. In particular, boundedness of the set of adjoint discrete solutions and upper semicontinuity of the locally adjoint mapping are proved. In the second part of paper an optimization problem described by convex inequality constraint is studied. By using the equivalence theorem concerning the subdifferential calculus and approximating method necessary and sufficient condition for discrete-approximation problem with inequality constraint is established.
AB - In the first part of the paperoptimization of polyhedral discrete and differential inclusions is considered, the problem is reduced to convex minimization problem and the necessary and sufficient condition for optimality is derived. The optimality conditions for polyhedral differential inclusions based on discrete-approximation problem according to continuous problems are formulated. In particular, boundedness of the set of adjoint discrete solutions and upper semicontinuity of the locally adjoint mapping are proved. In the second part of paper an optimization problem described by convex inequality constraint is studied. By using the equivalence theorem concerning the subdifferential calculus and approximating method necessary and sufficient condition for discrete-approximation problem with inequality constraint is established.
KW - discrete-approximation
KW - dual cone
KW - inequality constraint
KW - polyhedral
KW - Set-valued
KW - subdifferential
KW - uniformly bounded
KW - upper semicontinuous
UR - http://www.scopus.com/inward/record.url?scp=84868275601&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-31724-8_38
DO - 10.1007/978-3-642-31724-8_38
M3 - Conference contribution
AN - SCOPUS:84868275601
SN - 9783642317231
T3 - Communications in Computer and Information Science
SP - 364
EP - 372
BT - Advances in Computational Intelligence - 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012, Proceedings
T2 - 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU 2012
Y2 - 9 July 2012 through 13 July 2012
ER -