Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the Moon with minimum fuel expenditure. Or the dynamical system could be a nation's economy, with the objective to minimize unemployment; the controls in this case could be fiscal and monetary policy. A dynamical system may also be introduced to embed operations research problems within the framework of optimal control theory.
Model predictive control (MPC) is an advanced method of process control that is used to control a process while satisfying a set of constraints. It has been in use in the process industries in chemical plants and oil refineries since the 1980s. In recent years it has also been used in power system balancing models and in power electronics. Model predictive controllers rely on dynamic models of the process, most often linear empirical models obtained by system identification. The main advantage of MPC is the fact that it allows the current timeslot to be optimized, while keeping future timeslots in account. This is achieved by optimizing a finite time-horizon, but only implementing the current timeslot and then optimizing again, repeatedly, thus differing from a linear–quadratic regulator (LQR). Also MPC has the ability to anticipate future events and can take control actions accordingly. PID controllers do not have this predictive ability. MPC is nearly universally implemented as a digital control, although there is research into achieving faster response times with specially designed analog circuitry.
The general algebraic modeling system (GAMS) is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization problems. The system is tailored for complex, large-scale modeling applications and allows the user to build large maintainable models that can be adapted to new situations. The system is available for use on various computer platforms. Models are portable from one platform to another.
CUTEr is an open source testing environment for optimization and linear algebra solvers. CUTEr provides a collection of test problems along with a set of tools to help developers design, compare, and improve new and existing test problem solvers.
Sequential quadratic programming (SQP) is an iterative method for constrained nonlinear optimization which may be considered a quasi-Newton method. SQP methods are used on mathematical problems for which the objective function and the constraints are twice continuously differentiable, but not necessarily convex.
The TOMLAB Optimization Environment is a modeling platform for solving applied optimization problems in MATLAB.
In photogrammetry and computer stereo vision, bundle adjustment is simultaneous refining of the 3D coordinates describing the scene geometry, the parameters of the relative motion, and the optical characteristics of the camera(s) employed to acquire the images, given a set of images depicting a number of 3D points from different viewpoints. Its name refers to the geometrical bundles of light rays originating from each 3D feature and converging on each camera's optical center, which are adjusted optimally according to an optimality criterion involving the corresponding image projections of all points.
ADMB or AD Model Builder is a free and open source software suite for non-linear statistical modeling. It was created by David Fournier and now being developed by the ADMB Project, a creation of the non-profit ADMB Foundation. The "AD" in AD Model Builder refers to the automatic differentiation capabilities that come from the AUTODIF Library, a C++ language extension also created by David Fournier, which implements reverse mode automatic differentiation. A related software package, ADMB-RE, provides additional support for modeling random effects.
Augmented Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they replace a constrained optimization problem by a series of unconstrained problems and add a penalty term to the objective, but the augmented Lagrangian method adds yet another term designed to mimic a Lagrange multiplier. The augmented Lagrangian is related to, but not identical with, the method of Lagrange multipliers.
MOSEK is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constrained, conic and convex nonlinear mathematical optimization problems. The applicability of the solver varies widely and is commonly used for solving problems in areas such as engineering, finance and computer science.
NPSOL is a software package that performs numerical optimization. It solves nonlinear constrained problems using the sequential quadratic programming algorithm. It was written in Fortran by Philip Gill of UCSD and Walter Murray, Michael Saunders and Margaret Wright of Stanford University. The name derives from a combination of NP for nonlinear programming and SOL, the Systems Optimization Laboratory at Stanford.
WORHP, also referred to as eNLP by ESA, is a mathematical software library for numerically solving large scale continuous nonlinear optimization problems.
JModelica.org is a commercial software platform based on the Modelica modeling language for modeling, simulating, optimizing and analyzing complex dynamic systems. The platform is maintained and developed by Modelon AB in collaboration with academic and industrial institutions, notably Lund University and the Lund Center for Control of Complex Systems (LCCC). The platform has been used in industrial projects with applications in robotics, vehicle systems, energy systems, CO2 separation and polyethylene production.
APOPT is a software package for solving large-scale optimization problems of any of these forms:
MINOS is a Fortran software package for solving linear and nonlinear mathematical optimization problems. MINOS may be used for linear programming, quadratic programming, and more general objective functions and constraints, and for finding a feasible point for a set of linear or nonlinear equalities and inequalities.
Artelys Knitro is a commercial software package for solving large scale nonlinear mathematical optimization problems.
ANTIGONE, is a deterministic global optimization solver for general Mixed-Integer Nonlinear Programs (MINLP).
