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math.OC2023
Existence theorems for optimal solutions in semi-algebraic optimization
Jae Hyoung Lee, Gue Myung Lee, Tien Son Pham
Consider the problem of minimizing a lower semi-continuous semi-algebraic function on an unbounded closed semi-algebraic set…
math.OC2023
Subdifferentials at infinity and applications in optimization
Do Sang Kim, Minh Tung Nguyen, Tien Son Pham
In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Var…
math.OC2022
Characterizations of directional openness for set-valued mappings
Si Tiep Dinh, Tien Son Pham
We provide necessary and sufficient conditions for a set-valued mapping between finite dimensional spaces to be directionally open by relating this property with directional regula…