Preconference Workshop on Computational Optimization

Siddharth Agarwal, Ashutosh Mahajan, G. Chandra Mouli, Prashant Palkar, Rupak Rokade and Meenarli Sharma
IIT Bombay
This workshop will be held in three 90-minute sessions, each focussing on modeling and solving different types of optimization problems. Techniques will be described briefly so that more time is devoted to modeling and solving problems on a computer. Participants will be expected to install and run various solvers on a computer. The number of registrations is limited to 30. Basic knowledge of linear optimization and familarity with modeling linear programs is assumed. The details of the sessions are as follows.

1. Linear and nonlinear optimization
Simple realistic examples of different types of optimization problems: linear, quadratic and nonlinear programs will be modeled and solved using the FOSSEE Scilab Optimization Toolkit (FOT). Various ways of modeling a problem and setting solver parameters will be discussed. Demonstrations on how to understand solver outputs including duals will be given.

2. Mixed-integer nonlinear optimization
Algorithms for solving convex and nonconvex nonlinear problems with integer variables will be introduced with some motivating examples. Main components and design of solvers for such problems will be described using the open-source Minotaur solver as an example. Examples on how to combine various components for implementing customized algorithms will be demonstrated.

3. Derivative free optimization
Optimization problems for which evaluating the function values is expensive and derivative information is missing are quite challenging to solve even when the number of variables is small. A brief overview of such problems and some well known solvers will be presented. A novel approach called Constrained Scaled Conjugate Gradient Based Direct Search (CSCG-DS) will be discussed and demonstrated.

Supporting Material