Nonlinear Resource Allocation

We settled on the topic of solving the nonlinear resource allocation problem which can be formally stated as

\begin{array}{cll}<br /> \min &{\displaystyle \sum_{i=1}^n f_i(\xi_{i})} &\\[0.5em]<br /> {\rm s.t.} &{\displaystyle \sum_{i=1}^n g_i(\xi_i) \leq c}, & c \in \mathbb{R} \\[0.5em]<br /> & \ell_{i} \leq \xi_{i} \leq u_{i}, & i = 1,2 ,\ldots, n<br /> \end{array}

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

Continue reading » · Rating: · Written on: 10-09-08 · 2 Comments »

It’s Linear Programming, Not Linear Optimization!

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.

Continue reading » · Rating: · Written on: 09-01-08 · No Comments »