4 papers
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…
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…
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…
The bifurcation set of a real polynomial function of two variables and Newton polygons of singularities at infinity
Masaharu Ishikawa, Tat Thang Nguyen, Tien Son Pham
In this paper, we determine the bifurcation set of a real polynomial function of two variables for non-degenerate case in the sense of Newton polygons by using a toric compactifica…