Linear Programming

Pyomo (www.pyomo.org) is a mature and widely used Python library for expressing and solving a wide range of mathematical programs, i.e., algebraic optimization models. Pyomo allows users to specify optimization models with linear, non-linear (including differential algebraic and ordinary differential equations), mixed discrete-continuous, and stochastic components. These models can then be solved with a wide range of commercial and open source solvers, with varying capabilities.

In this series of lectures on continuous optimization, we introduce the area of optimizing over spaces of continuous variables, particularly vectors and matrices of real numbers. The talks will have an algorithmic focus, developing the theory necessary to describe the algorithms and understand their fundamental properties. After describing the landscape of problem types, and describing a few sample applications, we discuss some mathematical foundations in real analysis, convex analysis, and linear algebra.

In this talk we describe a mathematical model which couples the education
and labor markets, in which steady-steady competitive equilibria turn out to be characterized as the solutions to an infinite-dimensional linear program and its dual. In joint work with Erlinger, Shi, Siow and Wolthoff, we use ideas from optimal transport, to analyze this program and discover the formation of a pyramid-like structure with the potential to produce a phase transition separating singular from non-singular wage gradients.

Consider a region covered by sensors with a report of the number of agents within each sensor.
The question of the total number of agents, the minimum number of agents or the most likely number of agents
reported by these sensors will be discussed in terms of topology as well as hard problems within linear programming.
This talk is based on joint work with Bill Moran, Wang Zengfu, and Doug Cochran