Duality Consider the following LP: z = min 3x1 + 2x2 s.t. x1 + 3x2 4 2x1 + x2 1 x1 - x2 1 x1, x2 0. Suppose (x1, x2) (say, e.g. (2,1) is a feasible solution. Then we know that z 3x1 + 2x2(= 8), i.e. we get an upper bound. How can we get a lower bound (or
ISyE 6673 Financial Optimization Models
Shabbir Ahmed E-mail: sahmed@isye.gatech.edu Homepage: www.isye.gatech.edu/~sahmed
Topic: Immunization
Interest rate terminology
Spot rate: st is the (annual) interest rate on money held from time 0 until time t, i
Geometry of LPs Consider the following LP: min cfw_cT x | aT x bi i = 1, . . . , m. i The feasible region is X := cfw_x Rn | aT x bi i = 1, . . . , m i = m cfw_x Rn | aT x bi i=1 i
Xi
The Rn |
set Xi is a Half-space. The set Hi = cfw_x aT x = bi is a Hyp
ISyE 6673 Financial Optimization Models
Shabbir Ahmed E-mail: sahmed@isye.gatech.edu Homepage: www.isye.gatech.edu/~sahmed
Topic: Optimization Fundamentals
Outline
The generic optimization problem Properties of functions and sets Existence of optimal sol
ISyE 6673 Financial Optimization
Shabbir Ahmed E-mail: sahmed@isye.gatech.edu Homepage: www.isye.gatech.edu/~sahmed
Class Logistics
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