Nonlinear Programming

Excerpt

Chemical engineering applications have been a source of challenging optimization problems for over 50 years. For many chemical process systems, detailed steady state and dynamic behavior can now be described by a rich set of detailed nonlinear models, and relatively small changes in process design and operation can lead to significant improvements in efficiency, product quality, environmental impact, and profitability.With these characteristics, it is not surprising that systematic optimization strategies have played an important role in chemical engineering practice. In particular, over the past 35 years, nonlinear programming (NLP) has become an indispensable tool for the optimization of chemical processes. These tools are now applied at research and process development stages, in the design stage, and in the online operation of these processes. More recently, the scope of these applications is being extended to cover more challenging, large-scale tasks including process control based on the optimization of nonlinear dynamic models, as well as the incorporation of nonlinear models into strategic planning functions.

Moreover, the ability to solve large-scale process optimization models cheaply, even online, is aided by recent breakthroughs in nonlinear programming, including the development of modern barrier methods, deeper understanding of line search and trust region strategies to aid global convergence, efficient exploitation of second derivatives in algorithmic development, and the availability of recently developed and widely used NLP codes, including those for barrier methods [81, 391, 404], sequential quadratic programming (SQP) [161, 159], and reduced gradient methods [119, 245, 285]. Finally, the availability of optimization modeling environments, such as AIMMS, AMPL, and GAMS, as well as the NEOS server, has made the formulation and solution of optimization accessible to a much wider user base. All of these advances have a huge impact in addressing and solving process engineering problems previously thought intractable. In addition to developments in mathematical programming, research in process systems engineering has led to optimization modeling formulations that leverage these algorithmic advances, with specific model structure and characteristics that lead to more efficient solutions.

This text attempts to make these recent optimization advances accessible to engineers and practitioners. Optimization texts for engineers usually fall into two categories. First, excellent mathematical programming texts (e.g., [134, 162, 294, 100, 227]) emphasize fundamental properties and numerical analysis, but have few specific examples with relevance to real-world applications, and are less accessible to practitioners. On the other hand, equally good engineering texts (e.g., [122, 305, 332, 53]) emphasize applications with well-known methods and codes, but often without their underlying fundamental properties. While their approach is accessible and quite useful for engineers, these texts do not aid in a deeper understanding of the methods or provide extensions to tackle large-scale problems efficiently.