James Rohal

We settled on the topic of solving the nonlinear resource allocation problem which can be formally stated as
$$!\begin{array}{cll}
\min &{\displaystyle \sum_{i=1}^n f_i(\xi_{i})} &\\[0.5em]
{\rm s.t.} &{\displaystyle \sum_{i=1}^n g_i(\xi_i) \leq c}, & c \in \mathbb{R} \\[0.5em]
& \ell_{i} \leq \xi_{i} \leq u_{i}, & i = 1,2 ,\ldots, n
\end{array}$$

We will be applying several methods to solve this problem efficiently including interior point methods and a pegging algorithm.

I’ve begun meeting with my advisor Stephen Wright once a week. We are going to be looking at one of two possible topics:

1. Applying interior point methods to the resource allocation problem.
2. Tree-based decomposition methods in second-order-cone programming.

Oh, apparently the new trend is to refer to LP problems as LO problems.