We study mathematical programs with complementarity constraints. Several stationarity concepts, based on a piecewise smooth formulation, are presented and compared. The concepts are related to stationarity conditions for certain smooth programs as well as to stationarity concepts for a nonsmooth exact penalty function. Further, we present Fiacco-McCormick type second order optimality conditions and an extension of the stability results of Robinson and Kojima to mathematical programs with complementarity constraints.

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A guide to using the power of design flexibility to improve the performance of complex technological projects, for designers, managers, users, and analysts. Project teams can improve results by recognizing that the future is inevitably uncertain and that by creating flexible designs they can adapt to eventualities. This approach enables them to take advantage of new opportunities and avoid harmful losses. Designers of complex, long-lasting projects—such as communication networks, power plants, or hospitals—must learn to abandon fixed specifications and narrow forecasts. They need to avoid the “flaw of averages,” the conceptual pitfall that traps so many designs in underperformance. Failure to allow for changing circumstances risks leaving significant value untapped. This book is a guide for creating and implementing value-enhancing flexibility in design. It will be an essential resource for all participants in the development and operation of technological systems: designers, managers, financial analysts, investors, regulators, and academics. The book provides a high-level overview of why flexibility in design is needed to deliver significantly increased value. It describes in detail methods to identify, select, and implement useful flexibility. The book is unique in that it explicitly recognizes that future outcomes are uncertain. It thus presents forecasting, analysis, and evaluation tools especially suited to this reality. Appendixes provide expanded explanations of concepts and analytic tools.

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Recently, nonlinear programming solvers have been used to solve a range of mathematical programs with equilibrium constraints (MPECs). In particular, sequential quadratic programming (SQP) methods have been very successful. This paper examines the local convergence properties of SQP methods applied to MPECs. SQP is shown to converge superlinearly under reasonable assumptions near a strongly stationary point. A number of examples are presented that show that some of the assumptions are difficult to relax.