Constrained optimization

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# Constrained optimization - PowerPoint PPT Presentation

Constrained optimization. Indirect methods Direct methods. Indirect methods. Sequential unconstrained optimization techniques (SUMT) Exterior penalty function methods Interior penalty function methods Extended penalty function methods Augmented Lagrange multiplier method.

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## PowerPoint Slideshow about 'Constrained optimization' - mizell

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Presentation Transcript
Constrained optimization
• Indirect methods
• Direct methods
Indirect methods
• Sequential unconstrained optimization techniques (SUMT)
• Exterior penalty function methods
• Interior penalty function methods
• Extended penalty function methods
• Augmented Lagrange multiplier method
Exterior penalty function method
• Minimize total objective function=objective function+penalty function
• Penalty function: penalizes for violating constraints
• Penalty multiplier
• Small in first iterations, large in final iterations
• Sequence of infeasible designs approaching optimum
Interior penalty function method
• Minimize total objective function=objective function+penalty function
• Penalty function: penalizes for being too close to constraint boundary
• Penalty multiplier
• Large in first iterations, small in final iterations
• Sequence of feasible designs approaching optimum
• Needs feasible initial design
• Total objective function discontinuous on constraint boundaries
Extended interior penalty function method
• Incoprorates best features of interior and exterior penalty function methods
• Approaches optimum from feasible region
• Does not need a feasible initial guess
• Composite penalty function:
• Penalty for being too close to the boundary from inside feasible region
• Penatly for violating constraints