Review of last class
Operations that preserve convexity
nonnegative weighted sum
composition with affine function
pointwise maximum and supremum
composition
Minimization (Schur complement)
Perspective
The conjugate function
3. Convex functions
For dual pr

Review of last class
3. Convex functions
Examples: check convexity via second order condition
Quadratic function, quadratic over linear function
Log-sum-exponential function
Geometric mean function
Epigraph & sublevel set to show convexity
Jensens ineq

8. Geometric problems
Placement and facility locations
Classifiers: Support Vector Machine
Statistical Learning Theory
1
Perception and Intelligence Laboratory
School of Electrical Engineering at SNU
Placement and facility location
2
3
N points with coord

Review of Ch3
Definition of convex (concave) function
How to show the convexity of a function
Epigraph & sublevel set to show convexity
Operations that preserve convexity
nonnegative weighted sum
composition with affine function
maximum and supremum
c

Review of the last class
Perturbation and sensitivity analysis
global sensitivity
local sensitivity
Duality and problem reformulations
Introducing new variables and equality constraints
norm approximation problem
Implicit constraints
Dual Problems wi

Convex Optimization
Jin Young Choi
Dept. of Electrical and Computer Engineering
Seoul National University
Notice
Text : Convex Optimization,
Stephen Boyed,
Cambridge University Press
Evaluation: Homework 40%, Midterm 30%, Final 30%
F record for 3-times ab

Review of the last class
Quadratically constrained quadratic program (QCQP)
Second-order cone programming (SOCP)
Chebyshev center of a polyhedron
Robust Linear Programming
Deterministic Model
Stochastic Model
Geometric programming
Monomial
Posynomial

Review of the last class
Lagrange dual problem (example)
Weak and strong duality
Two-way partitioning
Slaters constraint qualification
Inequality form LP
Quadratic program
A nonconvex problem with strong duality
Geometric interpretation
Complementary sl

Review: Last Class
Lagrangian (definition)
Lagrange dual function
lower bound property of Lagrange dual function
Examples
Least-norm solution of linear equations
Standard LP problem
Equality constrained norm minimization
Lagrange dual and conjugate fun

Review of last class
Definition of convex (concave) function
Examples of convex (concave) function
Affine, exponential, powers, logarithm
Negative entropy, norm function, etc.
How to show the convexity of a function
Apply the definition
Restriction to

7. Statistical estimation & Filter design
maximum likelihood estimation
(Binary) hypothesis testing
Chebychev filter design
linear phase filter design
Convex Optimization
1
Perception and Intelligence Laboratory
School of Electrical Engineering at SNU
Par

Review of last class
How to show convexity of a set
Apply the definition of convexity
Operations that preserve convexity
intersection
affine functions
perspective function
linear-fractional functions
Generalized inequalities
Proper cone
Positive sem

6. Approximation and fitting
norm approximation
penalty function approximation
signal reconstruction
optimal control input design
Convex Optimization
1
Perception and Intelligence Laboratory
School of Electrical Engineering at SNU
Norm approximation
( A R

Review : 9. Unconstrained minimization
x ( k +1) = x ( k ) + t ( k ) x ( k )
x=
arg mincfw_f ( x)T v |=
v 1, f ( x + v) f ( x) + f ( x)T v;
minimize f ( x)
nsd
2
xsd =f ( x) * xnsd
f ( x)T v = f ( x)
*
xsd = f ( x),
. x 2 = ( x x)
T
xsd =
P 1f ( x), . x

Review: 4. Convex optimization problems
Formulation of optimization problem
Optimality condition
Typical types of convex optimization
quasiconvex optimization
linear optimization
quadratic optimization
geometric programming
Second order cone programm

Review of last class
2. Convex sets
Minimum and minimal elements in a convex set
Definition of the minimum element
Definition of a minimal element
Separating hyperplane theorem
Supporting hyperplane theorem
Dual cones and generalized inequalities
Dual i

11. Interior-point methods
inequality constrained minimization
logarithmic barrier function and central path
barrier method
feasibility and phase I methods
generalized inequalities
Convex Optimization
1
Perception and Intelligence Laboratory
School o

Review of last class
Definition of Convex/quasi-convex problem
Algorithm for Quasiconvex optimization
Transform into Bisection Convex problem
Linear program (LP)
Diet Problem
piecewise-linear minimization
(Generalized) linear-fractional program (Quasi-

Todays Keywords
Convex optimization solvers
Modelling system: transforming problems to standard form
Disciplined convex programming
CVX
Examples
Convex Optimization
1
Perception and Intelligence Laboratory
School of Electrical Engineering at SNU
Convex op