A robustification approach in unconstrained quadratic optimization

Abstract

Abstract. Unconstrained convex quadratic optimization problems subject to parameter perturbations are considered. A robustification approach is proposed and analyzed which reduces the sensitivity of the optimal function value with respect to the parameter. Since reducing the sensitivity and maintaining a small objective value are competing goals, strategies for balancing these two objectives are discussed. Numerical examples illustrate the approach.

Optimality conditions for robust weak sharp efficient solutions of nonsmooth uncertain multiobjective optimization problems

“…Remark 3. 3 We can see that the (CQ) defined in Definition 3.2 reduces to the constraint qualification defined in [39, Definition 3.2] when = R n . As well as, it is not hard to verify that this (CQ) reduces to the extended Mangasarian-Fromovitz constraint qualification (see [40]) in the smooth setting when = R n .…”

“…Theorem 4. 3 For the problem (UMP), let := R n . Assume that x 0 ∈ K satisfies the condition (3.11) with real numbers η and r .…”

“…Robust optimization has come out as a noticeable determinism framework for investigating mathematical programming problems with data uncertainty. Many researchers have been studied intensively both theoretical and applied aspects in the area of robust optimization; see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and the references therein.…”