ANALISIS MASALAH EKSTREM FUNGSI PADA RUANG BERNORMA

QURRATUL AINI, Dr. Ch. Rini

2011 | Tesis | S2 Matematika

Dalam tesis ini, dibahas tentang masalah ekstrem fungsi pada ruang bernorma. Pembahasan di awali dengan pengenalan himpunan konveks dan fungsi konveks pada ruang bernorma. Pembahasan pada himpunan konveks dan fungsi konveks meliputi definisi dan sifat-sifat dasar. Lebih lanjut dibahas mengenai fungsi lower semi-continuous dari atas, Transformasi Legendre-Fenchel dan subdiferensial dari fungsi konveks, dan kendala peminimum fungsi tujuan, serta dibuktikan Prinsip Variasional Ekeland dan Prinsip Variasional Borwein-Preiss Smooth.

In this thesis, we discuss about a point which minimize the value of a function on normed space in analysis. At first, we introduce the convex sets and the convex functions on normed space. The discussion in the convex set and the convex function including the definition and basic properties of them. Furthermore, we discuss the function that has lower semi-continuous from above, the Legendre-Fenchel transform and subdifferentials of convex functions, and the constraint of extreme functions, and we shall prove the Ekeland Variational Principle and the Borwein-Preiss Smooth Variational Principle.

Kata Kunci : Himpunana konveks, fungsi konveks, fungsi lower semi-continuous