Chapter 1 Linear Programming
1.1 Transportation of Commodities
We consider a market consisting of a certain number of providers
and demanders of a commodity and a network of routes between the
providers and the demanders along which the commodity can be s
Optimization I; Chapter 2
36
Chapter 2 Theory of Constrained Optimization
2.1 Basic notations and examples
We consider nonlinear optimization problems (NLP) of the form
minimize f (x)
over x lRn
subject to h(x) = 0
g (x) 0 ,
(2.1a)
(2.1b)
(2.1c)
where f :
Optimization I; Chapter 3
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Chapter 3 Quadratic Programming
3.1 Constrained quadratic programming problems
A special case of the NLP arises when the objective functional f is quadratic
and the constraints h, g are linear in x lRn . Such an NLP is called
Optimization I; Chapter 4
77
Chapter 4 Sequential Quadratic Programming
4.1 The Basic SQP Method
4.1.1 Introductory Denitions and Assumptions
Sequential Quadratic Programming (SQP) is one of the most successful methods
for the numerical solution of constr
Chapter 5 Convex Optimization in Function Space
5.1 Foundations of Convex Analysis
Let V be a vector space over lR and : V lR be a norm on V .
We recall that (V, ) is called a Banach space, if it is complete, i.e.,
if any Cauchy sequence cfw_vk lN of elem