@CsabaSzepesvari@prof_grimmer@TaeHo_Y00N This is known as the minimal displacement problem which has been studied in the fixed-point literature. I believe this is a different line of research from the outstanding work by @prof_grimmer and @TaeHo_Y00N, but I expect there may be some interesting hidden connections!
@CsabaSzepesvari@prof_grimmer@TaeHo_Y00N Hi, Csaba. Our paper with Roberto and Mario (https://t.co/Vl2r4krFv1) showed that for an L-Lipschitz map T:C->C in an arbitrary normed space (possibly L >1), residual can be reduced to max{0, c(1-1/L)} where c is the diameter of the convex domain C.
Every day, I try to jump into the problem by leaving other problems behind. It often feels like diving into the cold water. Hesitating to throw body, I dip my foot, but soon step out of the water shivering. After a struggle, I barely get into the water.
Today, I started a summer research internship at Vector Institute under the supervision of Amir-Massoud Farahmand. I had two great meetings and just love this place and the people. I'm ready to enjoy these four months at Vector Institute..!
I had a habit of solving problems only in my head. Recently, I felt that it just makes me a coward and rationalize my laziness. Unless I'm John von Neumann, writing formulas on paper and treating them by hand are healthy processes like kneading clay for making the bowl.
I spent two days understanding one inequality on paper. The truth is that I just missed a simple calculation. This often happens. While I cursed my negligence and lack of talent in my undergraduate years, now, with some desperation, I accept it as one of the essences of study.