Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available and that the constraint gradients are sparse.
We discuss an SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems. SNOPT is a particular implementation that makes use of a semidefinite QP solver. It is based on a limited-memory quasi-Newton approximation to the Hessian of the Lagrangian and uses a reduced-Hessian algorithm (SQOPT) for solving the QP subproblems. It is designed for problems with many thousands of constraints and variables but a moderate number of degrees of freedom (say, up to 2000). An important application is to trajectory optimization in the aerospace industry. Numerical results are given for most problems in the CUTE and COPS test collections (about 900 examples).

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SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization

This book is about the theoretical foundations of optimization algorithms, and also provides practical insights on how such methods should be implemented and applied. The goal of this text is not focused on in-depth details of state-of-the-art methods, but rather to provide a good foundation of the tried and trusted methods and how they can be used to solve real-world problems efficiently. The target audience for the text seems to be graduate students and engineers in industry as a good reference or self-study. However, it does not lend itself to easy adaption in a classroom setting due to the fact that only some chapters have problem sets and most chapters do not have a summary section. The book has four main parts each written by the one of the different authors. Two of the parts deal with standard unconstrained and constrained optimization techniques. The other two section deal with more complicated issues including solving problems that exhibit nonsmooth behavior and interior point methods. Solving optimization problems that have nonsmooth objectives or constraints is a formidable challenge because sensitivity information cannot be calculated using traditional approaches; the book provides a variety of ways to approach such problems. Interior point methods have been gaining popularity in the engineering optimization community for their efficiency and ability to maintain feasibility throughout the optimization process. There have been many textbooks written on the subject of numerical optimization. This book has the same flavor as many of these past books. A book with a very similar title by Nocedal and Wright [1] covered much of the same material, but it did not address nonsmooth problems. A classical book in the field by Flecther [2] considers nonsmooth problems but not interior point methods. Also, if one is more interested in comparing the performance of the various methods applied to engineering design problems, the book by Vanderplaats [3] may be more suitable. The appeal of this book is in the authors’ attention to detail and their advice on practical implementation issues. For many of the different optimization algorithms detailed flow charts are given. They also provide adequate examples to help the reader understand the methods better and explore possible pitfalls. There are, however, a few downsides of this book. The main one is that through translation of the book to English, it is evident that some of the finer points were lost and in some cases the text is hard to understand. The book could also have benefited from more figures; there are only 26. Finally, each of the dif

Numerical Optimization: Theoretical and Practical Aspects

http://egon.cheme.cmu.edu/Papers/BatchReviewMendezGrossmann.pdf

State-of-the-art review of optimization methods for short-term scheduling of batch processes

Model-based design of experiments for parameter precision: State of the art

http://cheresearch.engin.umich.edu/lin/publications/Continuous-time%20Versus%20Discrete-Time%20Approaches%20for%20Scheduling.pdf

Continuous-time versus discrete-time approaches for scheduling of chemical processes: a review

This paper considers the treatment of general equality and inequality path constraints in the context of the control vector parametrization approach to the optimization of dynamic systems described by mixed sets of differential and algebraic equations (DAEs) of index not exceeding 1. Equality path constraints are handled by incorporating as many of them as possible within the DAE system itself without increasing its index. This allows a subset of the control variables to be determined from the solution of the augmented DAE system. The issues involved in establishing an appropriate partitioning of the control variable vector are examined. Inequality path constraints are handled through the combined application of the discretization of these constraints at a finite number of points, and forcing an integral measure of their violation to zero. Numerical experiments demonstrating the advantages of this hybrid technique over its individual components are presented.

Solution of a Class of Multistage Dynamic Optimization Problems. 2. Problems with Path Constraints

A new strategy is proposed for the optimum design of chemical plants whose uncertain parameters are expressed as bounded variables. The design is such that the plant specifications will be met for any feasible values of the parameters while optimizing a weighted cost function which reflects the costs over the expected range of operation. The strategy is formulated as a nonlinear programme, and an efficient method of solution is derived for constraints which are monotonic with the parameters, a case which arises frequently in practice. The designs of a pipeline with a pump, of a reactor-separator system, and of a heat exchanger network, all with uncertain technical parameters, illustrate the effectiveness of the strategy for rational overdesign of a chemical plant.

Optimum design of chemical plants with uncertain parameters

Optimum Design of Multipurpose Chemical Plants

The optimal operation of mixed production facilities—a general formulation and some approaches for the solution

A robust version of the self-tuning regulator is developed. The regulator, which requires relatively little knowledge of system characteristics (estimated order of transfer function polynomials and an upper bound for transportation delays), has been shown to yield stable control and convergence for linear, time-invariant systems. Simulations and practical tests on a large pilot-scale process have shown that the inclusion of a variable forgetting factor and an “extended horizon” control criterion provides the regulator with a sufficient degree of robustness and flexibility to perform well in a nonlinear time-varying environment. The regulator makes use of intuitively easy-to-understand concepts and leaves few degrees of freedom for the potential user. Furthermore, extensive experiments and simulation studies have shown it to be insensitive to choice of initial conditions and dynamic characteristics set by the user.

R.W.H. Sargent

Papers

Solution of a Class of Multistage Dynamic Optimization Problems. 2. Problems with Path Constraints

Optimum design of chemical plants with uncertain parameters

Optimum Design of Multipurpose Chemical Plants

The optimal operation of mixed production facilities—a general formulation and some approaches for the solution

Theory and application of an extended horizon self‐tuning controller