Acta Mathematica Vietnamica
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ON CONTINUITY PROPERTIES OF THE SOLUTION MAP IN QUADRATIC PROGRAMMING
NGUYEN NANG TAMpp. 47-61
Abstract
We study in detail the lower semicontinuity and the upper semicontinuity properties of the set-valued map $(D,A,c,b)\to \mathrm{sol}(D,A,c,b),$ where $\mathrm{sol}(D,A,c,b)$ denotes the solution set of the quadratic programming problem
$$\text{Minimize } f(x):=c^Tx+\dfrac 12 x^TDx \text{ subject to }Ax\geq b,\ x\geq 0.$$
In particular, a complete characterization for the lower semicontinuity of the map $\mathrm{sol}(\cdot)$ is obtained.