How can an Inequality constraint - Lagrangian Multiplier in MATLAB

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Can you please share how the in-equality constraint is handled in MATLAB?
InequalityConsytaint.JPG
Basically, I want to know how the lambda * (constraint) == 0 and lambda>0 are added into solve command to solve simultaneously.
Equality constraint with lagrange multiplier has been handled in the following link.
However, request for approach how in-equality constraint can be handled.
Thanks in advance.

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