Lagrange Dual Problems with Linear Constraints on the Multipliers.
Abstract
Consider Lagrange dual problems in which the vector of Lagrange multipliers, in addition to the usual nonnegativity conditions, satisfies certain linear constraints. Of course, the maximum dual value, for such restricted classes of multipliers, need not equal the primal value, even if various constraint qualifications are appended. Obtain expressions for this maximum constrained dual value, in terms of perturbation functions for the primal convex program, and value functions associated with the linear constraints. At least some information on the primal perturbation functions appears to be necessary in order to put upper or lower bounds on the constrained dual value. For the case that the constraints are, simply, that a positive weighted sum of the multipliers shall not exceed some given bound (plus, of course, the usual nonnegativities), only two values of an associated one-dimensional perturbation function is needed to obtain such upper and lower bounds.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1978
- Accession Number
- ADA057430
Entities
People
- C. E. Blair
- Robert G. Jeroslow
Organizations
- Carnegie Mellon University