On Guarantee Optimization under Conditions of Integral Constraints on Control Actions and Nonterminal Quality Index**This work is supported by the Russian Foundation for Basic Re-search (11-01-12088-o_-m-2011), by the Program for State Support of Leading Scienti_c Schools of Russia (NSh-5927.2012.1), and by the Program of the Presidium of the Russian Academy of Sciences\Fundamental Problems of Nonlinear Dynamics in Mathematics and Physics” (12-P-1-1012).