## 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.