James Rohal » Mathematics http://jamesrohal.com Thu, 03 Sep 2009 18:35:10 +0000 en hourly 1 http://wordpress.org/?v=3.0.3 Nonlinear Resource Allocation http://jamesrohal.com/2008/10/09/nonlinear-resource-allocation/ http://jamesrohal.com/2008/10/09/nonlinear-resource-allocation/#comments Thu, 09 Oct 2008 20:36:06 +0000 Jim http://jamesrohal.com/?p=18 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.

]]> http://jamesrohal.com/2008/10/09/nonlinear-resource-allocation/feed/ 2 It’s Linear Programming, Not Linear Optimization! http://jamesrohal.com/2008/09/01/its-linear-programming-not-linear-optimization/ http://jamesrohal.com/2008/09/01/its-linear-programming-not-linear-optimization/#comments Tue, 02 Sep 2008 03:03:00 +0000 Jim http://jamesrohal.com/?p=9 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.

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