Why equality constraints are not a problem for Constrained optimization problems (some methods just ignore them and focus on inequalities)
Thank you!
Equality constraints in Optimization Problems
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optimization
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0If you have a constraint $h(x) = 0$, it could be equivalently rewritten as two inequality constraints $h(x) \le 0$ and $h(x) \ge 0$ – 2017-02-24
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0thanks! do you mean equality so to say reduces number of constraints? I'd like to ask why working with h(x)=0-like constraints much easier? – 2017-02-24
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0I think the only reason why authors omit equality constraints is to ease notation for their theory – 2017-02-24
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1Actually using $h(x)\geq0$ and $h(x)\leq0$ instead of $h(x)=0$ leads to constraint qualification failure and inapplicability of the Kuhn-Tucker approach. In my view a proper treatment of constrained optimization will deal with both types of constraints. It will come at the cost of notation, but the two types of constrains are not equivalent. – 2017-02-24
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0Basically every well-known theorem or algorithm handles equality different than inequality. Just in the introduction some authors drop the distinction in favor of notational convenience. But both types of constraints are fundamentally different. – 2017-02-25