Optimization





General

Sci-IPOpt

Sci-IPOpt is a library dedicated to non linear constrained optimization.

It can solve problems with sparse Gradient, Sparse Jacobian.

IpOpt is currently developed in the COIN-OR project.

IPOpt is a C++ set of classes.

SciNLOpt

This toolbox is an interface to the NLOpt optimization library

Features:

- A common interface for different algorithms— try a different algorithm just by changing one parameter.

- Support for large-scale optimization (some algorithms scalable to millions of parameters and thousands of constraints).

- Both global and local optimization algorithms.

- Algorithms using function values only (derivative-free) and also algorithms exploiting user-supplied gradients.

- Algorithms for unconstrained optimization, bound-constrained optimization, and general nonlinear inequality/equality
constraints.

Linear

Quapro

This toolbox defines linear quadratic programming solvers. The matrices defining the cost and constraints must be full, but the quadratic term matrix is not required to be full rank.

Features

• linpro : linear programming solver

• mps2linpro : convert lp problem given in MPS format to linpro format

• quapro : linear quadratic programming solver

Simplex optimization toolbox

This is the simplex optimization method which performs optimization of non linear function. This optimization method doesn’t use the derivative of the objective function.

There are 2 versions of the simplex:

– optim_nelder_mead: a classic script for optimization

– step_nelder_mead: the call to the objective function is done outside of the script.

Derivative Free

SciCOBYLA

SciCOBYLA is a derivative free non linear constrained optimization method.

Metaheuristics

Particle Swarm Optimization Toolbox

The PSO method, published by Kennedy and Eberhart in 1995, is based on a population of points at first stochastically deployed on a search field. Each member of this particle swarm could be a solution of the optimization problem. This swarm flies in the search field (of N dimensions) and each member of it is attracted by its personal best solution and by the best solution of its neighbours. Each particle has a memory storing all data relating to its flight (location, speed and its personal best solution). It can also inform its neighbours, i.e. communicate its speed and position. This ability is known as socialisation. For each iteration, the objective function is evaluated for every member of the swarm. Then the leader of the whole swarm can be determined: it is the particle with the best personal solution. The process leads at the end to the best global solution. This direct search method does not require any knowledge of the objective function derivatives

Particle Swarm Optimization Toolbox
The PSO method, published by Kennedy and Eberhart in 1995, is based on a population of points at first stochastically deployed on a search field. Each member of this particle swarm could be a solution of the optimization problem. This swarm flies in the search field (of N dimensions) and each member of it is attracted by its personal best solution and by the best solution of its neighbors. Each particle has a memory storing all data relating to its flight (location, speed and its personal best solution).
Unconstrained Optimization
The goal of this toolbox is to provide unconstrained optimization problems in order to test optimization algorithms.
The More, Garbow and Hillstrom collection of test functions is widely used in testing unconstrained optimization software. The code for these problems is available in Fortran from the netlib software archives.
Quapro
This toolbox defines linear quadratic programming solvers. The matrices defining the cost and constraints must be full, but the quadratic term matrix is not required to be full rank.

Features

– linpro: linear programming solver

– mps2linpro: convert lp problem given in MPS format to linpro format

– quapro: linear quadratic programming solver
Fmincon
The goal of this toolbox is to provide a fmincon function in Scilab. The fmincon function is a non-linearily constrained optimization solver. Currently, we use ipopt for the actual solver of fmincon. The current state of the function is experimental.

Many features are yet to be implemented. We provide upgraded versions of the optimset and optimget functions, which manage options which are required by fmincon.

Sci-IPOpt
This is the interface between Scilab and IPOpt, the solver for non linear constrained optimization problems.

Features:

The current module provides the following functions:

– ipopt : Scilab interface to the IPOpt optimizer.
SciNLOpt
This toolbox is an interface to the NLOpt optimization library, a common interface for many different algorithms. The users has to change only one parameter to study a different algorithm

– Support for large-scale optimization (some algorithms scalable to millions of parameters and thousands of constraints).

– Both global and local optimization algorithms.

– Algorithms using function values only (derivative-free) and also algorithms exploiting user-supplied gradients.

– Algorithms for unconstrained optimization, bound-constrained optimization, and general nonlinear inequality/equality
constraints.