Korea Advanced Institute of Science and Technology
convex opt
IE ie555

Fall 2015
Convex Optimization Boyd & Vandenberghe
3. Convex functions
basic properties and examples
operations that preserve convexity
the conjugate function
quasiconvex functions
logconcave and logconvex functions
convexity with respect to generalized ineq
Korea Advanced Institute of Science and Technology
convex opt
IE ie555

Fall 2015
Solutions to MATLAB Assignment 1
Introduction to Linear Algebra (Weeks 1 and 2)
Fall, 2015
1. (Reduced Row Echelon Form with Pivot Columns and Ranks)
In MATLAB, there are several useful commands for matrices such as rref command
which produces the reduced
Korea Advanced Institute of Science and Technology
convex opt
IE ie555

Fall 2015
THE DIRECTIONS DETERMINED BY n POINTS
IN THE PLANE
G. R. BURTON AND G. B. PURDY
1. Introduction
Let/() denote the minimum number of directions determined by n points in the
plane which are not all collinear. P. R. Scott [3] posed the problem of determinin
Korea Advanced Institute of Science and Technology
convex opt
IE ie555

Fall 2015
Complex Analysis, Problems set 1
1. Let z0 C. Prove by the denition of holomorphic function that
1
zz0
is holomorphic in C \ cfw_z0 .
2. Find the function v(x, y) conjugate to u(x, y) = x2 y 2 + x in C, i.e., u + iv is holomorphic in
C.
3. Let f be homomo
Korea Advanced Institute of Science and Technology
convex opt
IE ie555

Fall 2015
Complex Analysis, HW1, Due Sep. 9(Wed.), 5PM
1. Textbook Chapter1.4, problems 7, 12, 13, 19
2. Find all values for the following expressions.
(a) 5i
(b) tan1 (1 + i)
n
3. For sequences (fk ), (gk ) in C, we have
n
n
j=1
Prove using this summation by parts