Amenable Functions in Optimization

Résumé fourni par la source

Any optimization problem on IR n can be formulated as the minimization of an extended real-valued function f over all of IR n (i.e., https://www.w3.org/1998/Math/MathML" display="inline"> f : ℝ n → ℝ ¯ https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003580447/ce9022ba-af67-4a01-993e-cfddd27c6ae0/content/eq2736.tif "/> , where https://www.w3.org/1998/Math/MathML" display="inline"> ℝ ¯ : = ℝ ∪ { ∞ } https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003580447/ce9022ba-af67-4a01-993e-cfddd27c6ae0/content/eq2737.tif "/> . In this setting f is called the essential objective function for the problem, and the effective domain dom f := { x : f ( x ) <∞ } represents the set of feasible solutions.

Ce résumé expose les affirmations des auteurs. BNTIC ne l’interprète pas comme une validation indépendante des résultats.