Optimality conditions for constrained local optima, Lagrange multipliers and their use for sensitivity of optimal solutions . Constrained optimization. Inequality constraints. g2(x ). x 2. g1(x). Infeasible regions. Optimum. Decreasing f(x). x 1. Feasible region. Equality constraints.
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where j are unknown Lagrange multipliers
Warning: The default trust-region-reflective algorithm does not solve …. FMINCON will use the active-set algorithm instead.
Local minimum found ….
Optimization completed because the objective function is non-decreasing in feasible directions, to within the default value of the function tolerance, and constraints are satisfied to within the default value of the constraint tolerance.
x =10.0000 -0.0000
lambda = lower: [2x1 double]
upper: [2x1 double]
eqlin: [0x1 double]
eqnonlin: [0x1 double]
ineqlin: [0x1 double]
ineqnonlin: [2x1 double]
What assumption Matlab likely makes in selecting the default value of the constraint tolerance?
We would like to obtain derivatives of f* w.r.t. p
After manipulating governing equations we obtain
Lagrange multipliers called “shadow prices” because they provide the price of imposing constraints
Why do we have ordinary derivative on the left side and partial on the right side?