L. Vandenberghe
EE236B Winter 2015
Additional problem for homework #5
Generalized posynomials. In lecture 4 we dened a posynomial as a function of the form
m
f (x1 , . . . , xn ) =
a
xj ij ,
i
i=1
dom f = Rn ,
+
j=1,.,n
with i > 0. The exponents aij can t
L. Vandenberghe
EE236B Winter 2015
Homework assignment #1
This assignment is an introduction to the MATLAB software package CVX that will be
used in the course. CVX can be downloaded from www.cvxr.com.
Python users are welcome to use CVXPY (cvxpy.org) ins
Convex Optimization Boyd & Vandenberghe
6. Approximation and tting
norm approximation
least-norm problems
regularized approximation
robust approximation
61
Norm approximation
minimize
(A Rmn with m n,
Ax b
is a norm on Rm)
interpretations of solution
Convex Optimization Boyd & Vandenberghe
3. Convex functions
basic properties and examples
operations that preserve convexity
the conjugate function
quasiconvex functions
log-concave and log-convex functions
convexity with respect to generalized ineq
Convex Optimization Boyd & Vandenberghe
8. Geometric problems
extremal volume ellipsoids
centering
classication
placement and facility location
81
Minimum volume ellipsoid around a set
Lwner-John ellipsoid of a set C: minimum volume ellipsoid E s.t. C
Convex Optimization Boyd & Vandenberghe
7. Statistical estimation
maximum likelihood estimation
optimal detector design
experiment design
71
Parametric distribution estimation
distribution estimation problem: estimate probability density p(y) of a
ran
Convex Optimization Boyd & Vandenberghe
12. Interior-point methods
inequality constrained minimization
logarithmic barrier function and central path
barrier method
feasibility and phase I methods
complexity analysis via self-concordance
generalized
Convex Optimization Boyd & Vandenberghe
13. Conclusions
main ideas of the course
importance of modeling in optimization
131
Modeling
mathematical optimization
problems in engineering design, data analysis and statistics, economics,
management, . . . ,
Convex Optimization Boyd & Vandenberghe
1. Introduction
mathematical optimization
least-squares and linear programming
convex optimization
example
course goals and topics
nonlinear optimization
brief history of convex optimization
11
Mathematical o
Convex Optimization Boyd & Vandenberghe
2. Convex sets
ane and convex sets
some important examples
operations that preserve convexity
generalized inequalities
separating and supporting hyperplanes
dual cones and generalized inequalities
21
Ane set
l