On Nonconvex Optimization Problems with D.C. Equality and Inequality Constraints

作     者：Strekalovsky, Alexander S. 

作者机构：Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences Irkutsk664033 Russia 

出 版 物：《IFAC-PapersOnLine》 

年 卷 期：2018年第51卷第32期

页      面：895-900页

核心收录：

主　　题：Constraint theory Cost functions Linearization Numerical methods Optimization equality exact penalty Global optimality conditions Inequality constraint Kkt points linearized problem local serarch 

摘      要：The paper addresses the nonconvex nonsmooth optimization problem with the cost function and equality and inequality constraints given by d.c. functions. The original problem is reduced to a problem without constraints with the help of the exact penalization theory. After that, the penalized problem is represented as a d.c. minimization problem without constraints, for which the new mathematical tools under the form of global optimality conditions (GOCs) are developed. The GOCs reduce the nonconvex problem in question to a family of convex (linearized with respect to the basic nonconvexities) problems. In addition, the GOCs are related to some nonsmooth form of the KKT-theorem for the original problem. On the base of the developed theory we propose new numerical methods for local and global search. © 2018