Abstract
<p style='text-indent:20px;'>This paper aims at employing the image space approach to investigate the conjugate duality theory for general constrained vector optimization problems. We introduce the concepts of conjugate map and subdifferential by using two types of maximums. We also construct the conjugate duality problems via a perturbation method. Moreover, the separation condition is proposed by means of vector weak separation functions. Then, it is proved to be a new sufficient condition, which ensures the strong duality theorem. This separation condition is different from the classical regular conditions in the literature. Simultaneously, the application to a nonconvex multi-objective optimization problem is shown to verify our main results.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Control and Optimization,Strategy and Management,Business and International Management,Applied Mathematics,Control and Optimization,Strategy and Management,Business and International Management
Reference28 articles.
1. R. I. Bot, Conjugate Duality in Convex Optimization, Lecture Notes in Economics and Mathematical Systems, 637. Springer-Verlag, Berlin, 2010.
2. R. I. Bot, S. M. Grad, G. Wanka.New constraint qualification and conjugate duality for composed convex optimization problems, J. Optim. Theory Appl., 135 (2007), 241-255.
3. G. Castellani and F. Giannessi, Decomposition of mathematical programs by means of theorems of alternative for linear and nonlinear systems, In: Proc. Ninth Internat. Math. Programming Sympos., Budapest. Survey of Mathematical Programming, North-Holland, Amsterdam, 2 (1979), 423-439.
4. J. W. Chen, S. J. Li, Z. P. Wang, J. C. Yao.Vector variational-like inequalities with constraints: Separation and alternative, J. Optim. Theory Appl., 166 (2015), 460-479.
5. M. Chinaie, J. Zafarani.Image space analysis and scalarization of multivalued optimization, J. Optim. Theory Appl., 142 (2009), 451-467.