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Keywords:
ill-posed convex programs; regions of stability; Tihonov’s regularization; formulas for the marginal value; multicriteria decision making; minimal index set of binding constraints
ill-posed convex programs; regions of stability; Tihonov’s regularization; formulas for the marginal value; multicriteria decision making; minimal index set of binding constraints
Summary:
Regions of stability are chunks of the space of parameters in which the optimal solution and the optimal value depend continuously on the data. In these regions the problem of solving an arbitrary convex program is a continuous process and Tihonov's regularization is possible.
This paper introduces a new region we furnisch formulas for the marginal value. The importance of the regions of stability is demostrated on multicriteria decision making problems and in calculating the minimal index set of binding constraints in convex programming. These two nonlinear problems can be reduced to calculating a region of stability for a simple linear program. If Slater's condition holds, or for the rihgt hand side perurbations, the results reduce to the familiar ones.
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