Tight Feasibility Constraints in Engineering Design

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This research will assess the potential of a new method that tightly sandwiches nonlinear functions by piecewise linear functions, for efficiently finding solutions to optimization problems with tight feasibility constraints. A common class of problems in engineering design requires finding and optimizing functions that, over an interval, fit between narrowly separated lower and upper bounds. One typical example considers the components of a load-bearing beam or wire that has to fit into a narrow space between two existing surfaces and is to be optimized with respect to stiffness. Currently, such problems require extensive and expensive trial-and-error human intervention. The new theory and software tools will automate the search and make the trade-off between tolerances and computational budget explicit. The approach can be used in time-sensitive scenarios, such as interactive geometric design tools, and is expected to free computational cycles for the additional engineering objectives such as stiffness, heat conduction, uncertainty, cost or schedule. On a broader scale, the new tools will effectively extend existing computational geometry techniques to curved paths and surfaces. Tables, tools and tutorial examples will be disseminate as a part of the open-source SubLiME software library. The educational initiative will focus on adjusting the syllabus of undergraduate numerical computing to increase awareness of optimization problems; and to teach how to formulate and solve such problems. Aspects of the research to the general public will be communicated via two exhibitions featuring engineering analysis.