EE236A (Fall 2007-08)
Lecture 12 The barrier method
brief history of interior-point methods Newtons method for smooth unconstrained minimization logarithmic barrier function central points, the centr
EE236A (Fall 2007-08)
Lecture 11 The simplex method
extreme points adjacent extreme points one iteration of the simplex method degeneracy initialization numerical implementation
111
Idea of the simpl
EE236A (Fall 2007-08)
Lecture 9 Duality (part 1)
the dual of an LP in inequality form weak duality examples optimality conditions and complementary slackness Farkas lemma and theorems of alternatives
EE236A (Fall 2007-08)
Lecture 7 Applications in control
optimal input design robust optimal input design pole placement (with low-authority control)
71
Linear dynamical system
y (t) = h0u(t) + h1u(t
EE236A (Fall 2007-08)
Lecture 5 Structural optimization
minimum weight truss design truss topology design limit analysis design with minimum number of bars
51
Truss
m bars with lengths li and cross-
EE236A (Fall 2007-08)
Lecture 4 The linear programming problem
variants of the linear programming problem LP feasibility problem examples and some general applications linear-fractional programming
4
EE236A (Fall 2007-08)
Lecture 3 Geometry of linear programming
subspaces and ane sets, independent vectors matrices, range and nullspace, rank, inverse polyhedron in inequality form extreme points th
EE236A (Fall 2007-08)
Lecture 2 Linear inequalities
vectors inner products and norms linear equalities and hyperplanes linear inequalities and halfspaces polyhedra
21
Vectors
(column) vector x Rn: x1
EE236A (Fall 2007-08)
Lecture 1 Introduction and overview
linear programming example from optimal control example from combinatorial optimization history course topics software
11
Linear program (LP)
EE236A (Fall 2007-08)
Lecture 17 Integer linear programming
integer linear programming, 0-1 linear programming a few basic facts branch-and-bound
171
Denition
integer linear program (ILP) minimize cT
EE236A (Fall 2007-08)
Lecture 13 Convergence analysis of the barrier method
complexity analysis of the barrier method convergence analysis of Newtons method choice of update parameter bound on the to