Lagrange Multiplier Rules for Weak Approximate Pareto Solutions of Constrained Vector Optimization Problems in Hilbert Spaces - Zheng, Xi Yin; Li, Runxin (Journal of optimization theory and applications, 2014)
In the Hilbert space case, in terms of proximal normal cone and proximal coderivative, we establish a Lagrange multiplier rule for weak approximate Pareto solutions of constrained vector optimization problems. In this case, our Lagrange multiplier rule improves the main result on vector optimization in Zheng and Ng (SIAM J. Optim. 21: 886–911, 2011 ). We also introduce a notion of a fuzzy proximal Lagrange point and prove that each Pareto (or weak Pareto) solution is a fuzzy proximal Lagrange point.