Characterization of proper optimal elements with variable ordering structures
نویسندگان
چکیده
In vector optimization with a variable ordering structure the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications it was started to develop a comprehensive theory for these vector optimization problems. Thereby also notions of proper efficiency were generalized to variable ordering structures. In this paper we study the relation between several types of proper optimality. We give scalarization results based on new functionals defined by elements from the dual cones which allow complete characterizations also in the nonconvex case.
منابع مشابه
Properly optimal elements in vector optimization with variable ordering structures
In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions.
متن کاملOptimality conditions for approximate solutions of vector optimization problems with variable ordering structures
We consider nonconvex vector optimization problems with variable ordering structures in Banach spaces. Under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems. Using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...
متن کاملFRAGILITY CURVES FOR STRUCTURES EQUIPPED WITH OPTIMAL SATMDs
In this paper, a procedure has been presented to develop fragility curves of structures equipped with optimal variable damping or stiffness semi-active tuned mass dampers (SATMDs). To determine proper variable damping or stiffness of semi-active devices in each time step, instantaneous optimal control algorithm with clipped control concept has been used. Optimal SATMDs have been designed based ...
متن کاملFlexibility in Architecture: An Innovative Design for Covering of a Transformable Dome Using Kinetic Elements
Flexibility is a concept associated with variable needs of human beings.Today transformable structures are used to meet human changeable demands with different purposes and functions such as facades, roofs, sunshades, etc.A Flexible structure must be able to change physically and adapt to predetermined conditions.To provide flexibility and adaptability,transformable systems are required to poss...
متن کاملNumerical Procedures in Multiobjective Optimization with Variable Ordering Structures
Multiobjective optimization problems with a variable ordering structure instead of a partial ordering have recently gained interest due to several applications. In the last years a basic theory has been developed for such problems. The difficulty in their study arises from the fact that the binary relations of the variable ordering structure, which are defined by a cone-valued map which associa...
متن کامل