×

Quadratic growth and stability in convex programming problems with multiple solutions. (English) Zbl 0839.90090

The authors consider the problem of minimizing the function \(f(x)\) over \(x\in \mathbb{R}^n\), wehre \(f(x)= \max f_i(x)\), \(1\leq i\leq m\), with each \(f_i(x)\), \(i= 1,\dots, m\), convex and twice continuously differentiable. They give a second-order condition, called the second-order growth condition, involving the function \(f\) and the solution set \(S\) of the problem, which guarantees that the problem does not have a solution outside \(S\). This sort of condition is helpful in sensitivity analysis [see A. D. Ioffe, SIAM J. Optim. 4, No. 1, 1-43 (1994; Zbl 0820.90105)]. As an application, they discuss the stability of solutions in a convex constrained optimization problem.

MSC:

90C25 Convex programming
90C31 Sensitivity, stability, parametric optimization

Citations:

Zbl 0820.90105
PDFBibTeX XMLCite
Full Text: EuDML EMIS