Research in Scientific Computation - SERC

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Simplified Overview of SQP ● ● ● ● Major Iterations: QP subproblem to be solved and next iterated values of optimization variables must be found. Minor Iterations: iterations for QP subproblem to find a direction along which a Merit Function may be minimized with a step size along the direction. (postfeasibility test) Constraints are linearized and slacks added. Objective function is a Modified Lagrangian – a quadratic model involving the problem objective and departures of the constraints from linearity.
● ● Constraints in the QP subproblem QP subproblem is usually handled with either reduced gradient/reduce Hessian methods or with Schur Complement methods. In either approach, a working set of active linearized constraints is maintained. The constraint Jacobian can be column partitioned into – B Basis Matrix, S superbasics, N Nonbasics. – B should be square and invertible. – Superbasics represent degrees of freedom to minimize the objective function locally (satisfying the active constraints). – Nonbasics are stuck at bounds/some other values.
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Page 61: Further Research ● ● ● Onli

Research in Scientific Computation - SERC

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