# A Julia Ecosystem for Optimization

A modeling and solution environment for continuous optimization in the high-level and high-performance Julia language. The environment provides access to the CUTEst and AMPL modeling environments and can be used alongside JuMP.

Important features include lazy linear operators, a collection of Krylov methods, a problem collection, and interfaces to high-performance linear algebra kernels. Several building blocks for optimization are available and complete solvers are in the making.

# A Python Ecosystem for Optimization

A complete modeling and solution environment for continuous optimization in the high-level Python language with computationally-intensive parts written in Cython. Distributed across several modular packages, the environment features modeling facilities, including automatic differentiation, limited-memory quasi-Newton approximations, discretized PDE-constrained problems via FEniCS, building blocks for writing optimization solvers, efficient linear algebra functionalities, and several complete solvers.

# LLDL: Limited-Memory LDL Factorization

LLDL implements a limited-memory scheme for symmetric matrices that possess a \(LDL^T\) factorization, i.e., with \(D\) diagonal. Symmetric quasi-definite matrices fall into this category. LLDL is applicable to symmetric indefinite matrices that are not quasi definite, or more generally do not admit a \(LDL^T\) factorization. In this case, it computes an incomplete factorization of a nearby matrix. LLDL is chiefly used to produce preconditioners for solving symmetric indefinite systems using an iterative method such as MINRES.

# CUTEr / CUTEst

A versatile testing environment for optimization and linear algebra solvers. The package contains a collection of test problems, along with Fortran 77, Fortran 90/95, C/C++ and Matlab tools intended to help developers design, compare and improve new and existing solvers. It is usually associated to SIFDecode, a decoder for problems modeled in the SIF—a generalization of the MPS modeling language for linear programs. CUTEst realizes the interface between such problems and a variety of popular solvers.

# GALAHAD

A thread-safe library of Fortran 90 packages for nonlinear optimization problems. Areas currently covered by the library include unconstrained and bound-constrained optimization, quadratic programming, nonlinear programming, systems of nonlinear equations and inequalities, and nonlinear least squares problems. The library also contains a quadratic program preprocessor and a Lanczos-based method for trust-region subproblems.