0434234 20240103204934.120141124235959.9 84911059522 000344748000027 10.1137/130948070 30 s. P cav_un_epca*02575960363-0129525 (2014)3371-3400SIAM Society for Industrial and Applied Mathematics shape optimization contact problems Coulomb friction solution-dependent coefficient of friction mathematical programs with equilibrium constraints cav_un_auth*0212850 Beremlijski P. CZ cav_un_auth*0101173 Outrata Jiří UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0211704 Haslinger J. CZ cav_un_auth*0281511 Pathó R. CZ http://library.utia.cas.cz/separaty/2014/MTR/outrata-0434234.pdf GAP201/12/0671 GA ČR CZ cav_un_auth*0289475 CZ.1.05/1.1.00/02.0070 GA MŠK CZ cav_un_auth*0309973 CZ.1.07/2.3.00/20.0070 GA MŠK CZ cav_un_auth*0310061 The present paper deals with shape optimization in discretized two-dimensional (2D) contact problems with Coulomb friction, where the coefficient of friction is assumed to depend on the unknown solution. Discretization of the continuous state problem leads to a system of finite-dimensional implicit variational inequalities, parametrized by the so-called design variable, that determines the shape of the underlying domain. It is shown that if the coefficient of friction is Lipschitz and sufficiently small in the C0,1-norm, then the discrete state problems are uniquely solvable for all admissible values of the design variable (the admissible set is assumed to be compact), and the state variables are Lipschitzian functions of the design variable. This facilitates the numerical solution of the discretized shape optimization problem by the so-called implicit programming approach. BA 2015 4 RVO:67985556 http://hdl.handle.net/11104/0239356 cav_un_auth*0295947 Vysoká škola báňská - Technická univerzita Ostrava VŠB CZ cav_un_auth*0296304 Matematicko-fyzikální fakulta KU MFF KU CZ S AUTOMATIONCONTROLSYSTEMS|MATHEMATICSAPPLIED 1.443 1.615 Q1 89.021 69.081 Q1* Q1* 2014 84911059522 SCOPUS 000344748000027 WOS cav_un_epca*0257596 SIAM Journal on Control and Optimization 0363-0129 1095-7138 Roč. 52 č. 5 2014 3371 3400 SIAM Society for Industrial and Applied Mathematics