Convex operators 
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Teaching Staff in Charge 
Prof. NEMETH Alexandru, Ph.D., nemab@math.ubbcluj.ro 
Aims 
The investigation of the convex operators is the central question of the vectorial convex analysis. Although a new domain, an extended monography is concerned about it (see the literature). The lectures will cover the background of the domain emphasizing about the subdifferential calculus of the convex operators.

Content 
Will be revisited some fundamental results forom the geometry of convex sets in topological vector spaces. It will be introduced the notion of the convex correspondence. The convex operator is a mapping from a vector space into an ordered vector space satisfying the convexity inequality with respect to the order relation of the adress space. When the adress space is a latticially complete ordered vector space, the convex operators have good subdifferentiability properties, expressed by the HahnBanachKantorovich theorem. The fully subdifferentiability property is requiring weaker property of the adress space. This property is related with the weak HahnBanach extension property and is valid for ordered regular topological vector spaces. All these questions will be covered by the course. 
References 
1. A.G. Kusraev, S.S. Kutateladze: Subdifferencial'nye iscislenie, Novosibirsk, 1983.
2. A.G. Kusraev, S.S. Kutateladze: Subdifferentials: Theory and Applications, Kluwer, Doderecht, 1995. 3. A.B. Nemeth: Convex operators: Some subdifferentiability results, Optimization, 1992, Vol 23, pp. 275301. 
Assessment 
Exam. 