Invited Session Thu.1.H 1058

Thursday, 10:30 - 12:00 h, Room: H 1058

Cluster 10: Implementations & software [...]

Modeling languages and software I


Chair: Robert Fourer



Thursday, 10:30 - 10:55 h, Room: H 1058, Talk 1

John D. Siirola
Modeling and optimizing block-composable mathematical programs in Pyomo

Coauthors: William E. Hart, Jean-Paul Watson


Computational tools for modeling mathematical programs are in wide-spread use within both academia and industry. However, available commercial and open-source software packages broadly lack capabilities for specifying, manipulating, and solving hierarchically structured mathematical programs, e.g., in which sub-blocks of variables and constraints are manipulated and composed to form a more complex, higher-level optimization model (ASCEND [ ] and [ ] are notable exceptions). Our experience with real-world optimization applications indicates that this modeling capability is critical, in methodological contexts ranging from stochastic programming to generalized disjunctive programming, and in application contexts such as electrical grid operations and planning problems. In this talk, we discuss mechanisms for expressing, manipulating, and solving hierarchically or block structured mathematical programs available in the Pyomo open-source Python modeling environment and distributed as part of the broader Coopr project for optimization. We motivate the need for this capability using a variety of illustrative examples.



Thursday, 11:00 - 11:25 h, Room: H 1058, Talk 2

Guillaume Sagnol
PICOS: A python interface to conic optimization solvers


PICOS is a new user-friendly modeling language written
in python, which interfaces
several conic and integer programming solvers,
similarly to YALMIP under MATLAB.
PICOS offers the possibility to
enter an optimization problem as a high level model,
and to solve it with several different solvers.
This can be very useful to quickly implement some models and
test their validity on simple examples.
Furthermore, with PICOS one can take advantage of the
python programming language to easily read and write data,
construct a list of constraints by using list comprehensions,
take slices of multidimensional variables,~ …
In this talk, I will give a tutorial on PICOS,
showing how to enter different optimization problems such as
linear programs (LP), mixed integer programs (MIP),
second order cone programs (SOCP), semidefinite programs (SDP),
quadratically constrained quadratic programs (QCQP) or
geometric programs (GP) in PICOS, and how to solve these problems
with several solvers, including cvxopt, scip, mosek and cplex.



Thursday, 11:30 - 11:55 h, Room: H 1058, Talk 3

Robert Fourer
Strategies for using algebraic modeling languages to formulate second-order cone programs

Coauthor: Jared Erickson


A surprising variety of optimization applications can be written as convex quadratic problems that linear solvers can be extended to handle effectively. Particular interest has focused on conic constraint regions and the "second-order cone programs'' (or SOCPs) that they define. Whether given quadratic constraints define a convex cone can in principle be determined numerically, but of greater interest are the varied combinations of sums and maxima of Euclidean norms, quadratic-linear ratios, products of powers, p-norms, and log-Chebychev terms that can be identified and transformed symbolically. The power and convenience of algebraic modeling language may be extended to support such forms, with the help of a recursive tree-walk approach that detects and converts arbitrarily complex instances - freeing modelers from the time-consuming and error-prone work of maintaining the equivalent SOCPs explicitly. These facilities moreover integrate well with other common linear and quadratic transformations. We describe the challenges of creating the requisite detection and transformation routines, and report computational tests using the AMPL language.


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