Akademik Dersler - Tanıtım


Code - Course Title	MAT540 - Introduction to Convex Analysis
Course Type	Elective Courses
Language of Instruction	Türkçe
Laboratory + Practice	3+0
ECTS	7.5
Course Instructor(s)	DOKTOR ÖĞRETİM ÜYESİ SAMET BİLA
Mode of Delivery	The mode of delivery of this course is only Face to face
Prerequisites	There is no prerequisite or co-requisite for this course.
Courses Recomended	Analysis I, Analysis III, Functional Analysis I,II
Required or Recommended Resources	Hiriart-Urruty J.-B, Lemarechal C., Fundamentals of Convex Analysis, Springer Verlag, Berlin, 2001.B.S. Mordukhovich, N.M. Nam, An Easy Path to Convex Analysis and Applications, Morgan & Claypool, 2014.
Recommended Reading List	Lay S.R., Convex Sets and their Applications, Wiley & Sons, 1982.Roberts A.W., Varberg D.E., Convex Functions, Academic Press, 1973.Rockafellar R.T., Convex Analysis, Princeton university Press, 1970.
Assessment methods and criteria	Written exam
Work Placement	N/A
Sustainability Development Goals

Weeks	Topics
Week - 1	Affine sets and hyperplanes
Week - 2	Convex sets and convexity preserving operations on sets
Week - 3	Caratheodory’s theorem
Week - 4	Topological properties of convex sets
Week - 5	Seperation theorems for convex sets
Week - 6	Supporting hyperplanes and extreme points
Week - 7	Definition of a convex function and some characterizations
Week - 8	Fundamental properties of convex functions
Week - 9	Functional operations preserving convexity
Week - 10	Continuity of convex functions
Week - 11	Differentiability of convex functions
Week - 12	Support functions and sublinearity
Week - 13	The concept of subdiferantial of convex functions
Week - 14	The concept of subdifferantial of convex functions and some basic properties

Assessment Method and Passing Requirements
	Quamtity	Percentage (%)
Toplam (%)		0