Sensitivity Analysis for Convex Multiobjective Programming in Abstract Spaces

Abstract

The main object of this paper is to prove that for a linear or convex multiobjective program, a dual program can be obtained which gives the primal sensitivity without any special hypothesis about the way of choosing the optimal solution in the efficient set. ᮊ

Sensitivity of Pareto Solutions in Multiobjective Optimization

“…Since instead of q j , q we can consider any parameter or group of parameters in (10), this continuity argument proves the following fact. …”

“…This necessitated studies on the sensitivity of multiobjective programs (Refs. [6][7][8][9][10][11], with respect to perturbations of objective functions, or utility functions, or the ordering cone (Ref. 8) to analyze the stability of solutions under certain assumptions like convexity (Ref.…”

“…8) to analyze the stability of solutions under certain assumptions like convexity (Ref. 10) or homogeneity (Ref. 11) or under some particular quantitative assumptions (Ref.…”

“…In order to overcome these difficulties, the recent literature (see for instance Refs. [3][4][5][6][7][8][9][10][11][22][23][24][25][26] has developed new ideas and methods; we try to show here that the balance space approach may be a useful alternative and can broaden possible techniques. Since the adjoint Pareto set equals the ideal point J plus the balance set [P * = f (P ) = J + B (see Refs.…”

Measuring the Balance Space Sensitivity in Vector Optimization

“…In fact, statements are far more complicated than the corresponding results for scalar problems, and their practical applications present larger difficulties too. Linear vector problems are mucb easier but, as pointed out in [1] and [4], even this case becomes complex when using flexible criteria to choose an optimal solu tion in the efficient set 2 In order 1,0 overcome these difficulties the recent literature (see for instance [2], [3], [11] or [12]) has developed new ieleas anel methods, anel we will try to show here that the balance space approach may be an useful alternative anel can broaden possible techniques. Most of the classical caveats disappear…”