MCAA: Applied Matrix-free Constrained Nonlinear Programming Problems and Algorithms to Approximate their Solution

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This proposal outlines a program to develop a class of matrix-free algorithms for the solution of nonlinearlyconstrained optimization problems. Of special interest are problems arising in modeling and simulation ofindustrially important materials. Numerical algorithms will be developed, implemented and tested, and thenreleased as public domain software. These matrix-free algorithms will, in turn, be employed as educational tools. In particular, when teaching numerical methods (like Finite Element or Finite Difference Methods) in undergraduate classes, these methods will be used to shift the emphasis away from linear-algebraic issues (like building mass and stiffness matrices) allowing a stronger emphasis to be placed on methodology. The linear-algebraic details can then be left for more advanced classes.