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Elucidating the Geometry of Constrained Nonlinear Optimization With Symbolic Linear Algegra

Frank Kampas
Organization: Physicist at Large Consulting
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The mathematics behind various nonlinear optimization techniques can be obscured by the details of the numerical methods used to reach the solution. Using symbolic matrix functions and symbolic solution of the optimization conditions it is possible to make the fundamentals of various techniques more transparent. Four different techniques are described. Two of them, the Karush- Kuhn-Tucker equations and a Jacobian Minors approach, use the fact that the objective function gradient lies in the space of the constraint functions gradients. The other two, using a tangent space basis set or a tangent space projection operator, use the fact that the objective function gradient has no component in the constraint tangent space.

*Applied Mathematics > Optimization
*Mathematics > Algebra > Linear Algebra
*Mathematics > Geometry > n-Dimensional Geometry

Optimization Nonlinear Symbolic
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symbolic_optimization.nb (400.4 KB) - Mathematica Notebook