On quadratic scalarization of vector optimization problems in Banach spaces

Abstract

We study vector optimization problems in partially ordered Banach spaces and suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We discuss the so-called adaptive scalarization of such problems and show that the corresponding scalar non-linear optimization problems can be by-turn approximated by quadratic minimization problems.

Keywords:

• vector-valued optimization
• lower semicontinuity
• partial-ordered spaces
• efficient solutions
• scalarization approach

AMS Subject Classifications:

• 90C29
• 90C55
• 90C48
• 46B40