Mathematics I
HSG Master Mathematics
HSG Master Mathematics
HAMILTONIAN
What are the assumptions for the Hamiltonian?
Continously differentiablilty
HAMILTONIAN
How to construct the Hamiltonian?
4 conditions:
HAMILTONIAN
When is the global optimal solution also sufficent?
Concavity
HAMILTONIAN
What is the Transversality condition?
The transversality condition requires the present value of the state variables to converge to zero as the planning horizon recedes towards infinity. The first-order and transversality conditions are sufficient to identify an optimum in a concave optimization problem. Given an optimal path, the necessity of the transversality condition reflects the impossibility of finding an alternative feasible path for which each state variable deviates from the optimum at each time and increases discounted utility
CONVEXITY
Examples of convex and concave functions?
They are convex/concave if:
Convexity
When are functions convex/concave?
Twice differentiable
CONVEXITY
When is a matrix convex or concave?
Convex, concave
CONVEXITY
When are sums convex/concave?
If:
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Cartes-fiches
HAMILTONIAN
What are the assumptions for the Hamiltonian?
Continously differentiablilty
HAMILTONIAN
How to construct the Hamiltonian?
4 conditions:
HAMILTONIAN
When is the global optimal solution also sufficent?
Concavity
HAMILTONIAN
What is the Transversality condition?
The transversality condition requires the present value of the state variables to converge to zero as the planning horizon recedes towards infinity. The first-order and transversality conditions are sufficient to identify an optimum in a concave optimization problem. Given an optimal path, the necessity of the transversality condition reflects the impossibility of finding an alternative feasible path for which each state variable deviates from the optimum at each time and increases discounted utility
CONVEXITY
Examples of convex and concave functions?
They are convex/concave if:
Convexity
When are functions convex/concave?
Twice differentiable
CONVEXITY
When is a matrix convex or concave?
Convex, concave
CONVEXITY
When are sums convex/concave?
If:
