Study On Radius Of Robust Feasibility And Robust Error Bounds For Uncertain Convex Optimization Problems

Robust optimization is widely used in management,economy,automation,system science and engineering technology.The robust feasible radius is the maximum value to guarantee the non-empty robust feasible set of the uncertain inequality system.The robust error bound plays a key role in the sensitivity analysis and convergence analysis of the algorithm.So,it is of great practical significance to study the robust feasible radius and the robust global error bound of the uncertain system.In view of this,this paper mainly focuses on the calculation formula of robust feasible radius for uncertain convex cone programming and the characterization of robust error bounds for uncertain convex inequality systems.The main research contents are as follows:The robust optimization method is used to study a class of uncertain convex cone programming.This paper gives the formula for calculating the robust feasible radius under different data uncertainty sets.Firstly,this paper gives the definitions and properties of admissible set and epigraph set of uncertain convex cone programming.Then,with the help of the distance formula from the origin to the epigraph,this paper provided the upper and lower bounds of the robust feasible radius for the convex cone programming with uncertain data in the ball set and the robust feasible radius formula for the SOS-convex polynomial constrained robust optimization problem.In addition,an exact formula for the robust feasible radius of convex cone programming with piecewise linear function constraints with uncertain data in a box or polyhedral uncertain set is given.Finally,the range of admissible set and the robust feasible radius of uncertain system are calculated by some simple examples.The exact formula of the robust feasible radius of uncertain convex cone programming can provide a theoretical basis for the calculation of related programs,so as to solve related practical applications.Robust global error bounds for uncertain convex inequality systems are characterized from several angles.By using the right derivative of the boundary points of the solution set,the projection operator from the origin to the solution set,and the duality condition,this paper mainly gives the equivalent characterization of robust global error bounds for uncertain convex inequality systems.Then,the necessary conditions for robust global error bounds of uncertain convex inequality systems are given by the properties of recovery function and conjugate function.Finally,the duality condition is not a sufficient condition but a necessary condition for the existence of robust error bounds.