General nonlinear optimization problems are difficult to solve. Depending on particular optimization algorithm, they may require tuning parameters, providing derivatives, adjusting scaling, and trying multiple starting points. Convex optimization problems do not have any of those issues and are thus easier to solve. The challenge is that these problems must meet strict requirements. Even for candidate problems with the potential to be convex, significant experience is usually needed to recognize and utilize techniques that reformulate the problems into an appropriate form.

As mentioned in Chapter 8, apart from the ‘general exceptions’ and the ‘security exceptions’, discussed in that chapter, WTO law also provides for ‘economic emergency exceptions’. These exceptions allow Members to adopt two types of measures, otherwise WTO-inconsistent, namely, ‘safeguard measures’ and ‘balance-of-payments measures’. This chapter deals in turn with: (1) safeguard measures under the GATT 1994 and the Agreement on Safeguards; (2) safeguard measures under other WTO agreements; and (3) balance-of-payments measures under the GATT 1994 and the GATS.

Engineering design optimization problems are rarely unconstrained. In this chapter, we explain how to solve constrained problems. The methods in this chapter build on the gradient-based unconstrained methods fromand also assume smooth functions. We first introduce the optimality conditions for a constrained optimization problem and then focus on three main methods for handling constraints: penalty methods, sequential quadratic programming (SQP), and interior-point methods.

This part of the book considers how to study the work of a poet. It uses the poets Emily Brontë and Srinivas Rayaprol as case studies to illustrate how to build up a picture of a poet’s career, how to get to grips with their central interests and their ways of addressing them, and how to develop a response to a writer in the context of the broader critical debate around their work.

Most algorithms in this book assume that the design variables are continuous. However, sometimes design variables must be discrete. Common examples of discrete optimization include scheduling, network problems, and resource allocation. This chapter introduces some techniques for solving discrete optimization problems.

While professing support for trade liberalisation, trade policymakers often insist that international trade should be ‘fair’. ‘Unfair’ trade comes in many forms and guises. Unfair trade practices may include cartel agreements, price fixing, and the abuse of a dominant position on the market.1 WTO law, at present, does not provide for rules on these and many other particular forms of unfair trade. This absence of rules partly reflects a lack of agreement on what are ‘fair’ and ‘unfair’ trade practices. WTO law provide for detailed rules with respect to dumping and certain types of subsidisation – two specific trade practices commonly considered to be ‘unfair’. Members differ in opinion as to what extent these trade practices are truly ‘unfair’. This difference in opinion among Members reflects differences in their societies in general and their economic systems in particular.

This section outlines the contents and purpose of the book. It asks why we should read poetry, what a poem is, and how we can connect with poems and understand and enjoy them.

In the introductory chapter, we discussed function characteristics from the point of view of the function’s output—the black-box view shown in Fig. 1.16. Here, we discuss how the function is modeled and computed. The better your understanding of the model and the more access you have to its details, the more effectively you can solve the optimization problem. We explain the errors involved in the modeling process so that we can interpret optimization results correctly.