2198. Entropy Optimization using Convex Methods and Piecewise Linear Approximation
Invited abstract in session WC-4: Bilevel and Mixed-Integer Nonlinear Programming, stream Continuous and Global Optimization.
Wednesday, 13:30-15:00Room: H6
Authors (first author is the speaker)
| 1. | Paula Franke
|
Abstract
Understanding statistical dependencies in biological sequence data can provide valuable insights for future treatments for viral diseases, for example HIV. The presentation covers the analysis and optimization of a real-valued entropy function for matrices as an analytical tool for virus studies. Specifically, we present a computational means to compare observed entropy values to the highest and lowest possible while maintaining normalized marginal distributions. The maximization problem can be rewritten as a convex minimization problem. Here, we show that the solution is bounded away from the nonsmooth part of the function, allowing for the implementation of a gradient-based solver. In the concave case, the entropy function is approximated by piecewise linear functions that are refined based on maximal error. This approach yields the implementation of an IP-formulation using SOS2-constraints. The convex and concave programs use the off-the-shelf solvers IPOPT and Gurobi, respectively, and are validated with test data points. Limitations of the implementations, in particular numerical accuracy, and validation through other methods are discussed and we will argue the reasonableness of the obtained results.
Keywords
- Continuous Optimization
- Non-smooth Optimization
- Nonlinear Programming
Status: accepted
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