A continuous extension that preserves concavity, monotonicity and Lipschitz continuity
Year: 2003
Type: report
Abstract: The following is proven here: let W : X � C −→ R, where X is convex, be a continuous and bounded function such that for each y ∈ C, the function W (�, y) : X −→ R is concave (resp. strongly concave; resp. Lipschitzian with constant M; resp. monotone; resp. strictly monotone) and let Y ⊇ C. If C is compact, then there exists a continuous extension of W , U : X � Y −→ �infX�C W, supX�C W �, such that for each y ∈ Y , the function U (�, y) : X −→ R is concave (resp. strongly concave; resp. Lipschitzian with constant My ; resp. monotone; resp. strictly monotone).
DOI: 10.32468/be.230
Author: Andrés Carvajal
Institution: Brown University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2129848733