In this article we provide weak sufficient strong duality conditions for a convex optimization problem with cone and affine constraints, stated in infinite dimensional spaces, and its Lagrange dual problem. Our results are given by using the notions of quasi-relative interior and quasi-interior for convex sets. The main strong duality theorem is accompanied by several stronger, yet easier to verify in practice, versions of it. As exemplification we treat a problem which is inspired from network equilibrium. Our results come as corrections and improvements to Daniele and Giuffré (2007) . © 2009 Elsevier Inc. All rights reserved.
Grad, A. (2010). Quasi-relative interior-type constraint qualifications ensuring strong Lagrange duality for optimization problems with cone and affine constraints. Journal of Mathematical Analysis and Applications, 361(1), 86–95. https://doi.org/10.1016/j.jmaa.2009.09.006