Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Applied & computational complex analysis: power series integration conformal mapping location of zero
Newton's Method for a Class of Optimal Shape Design Problems
SIAM Journal on Optimization
Linear Programming and Network Flows
Linear Programming and Network Flows
An adjoint approach to optimal design of turbine blades
Applied Numerical Mathematics - Tenth seminar on and differential-algebraic equations (NUMDIFF-10)
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The problems of optimization of cylindrical bar cross-sections are formulated in variational forms. The functional considered characterizes torsional and bending rigidities, and the area of cross-section of the bar. The shape of the boundary of the cross-section is taken as a design variable. The problem is first expressed as an optimal control problem. Then by using an embedding method, the class of admissible shapes is replaced by a class of positive Borel measures. The optimization problem in measure space is then approximated by a linear programming problem. The optimal measure representing optimal shape is approximated by the solution of this finite dimensional linear programming problem. Numerical examples are also given.