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Solving constrained optimization problem: projected gradient vs. dual?

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I recently got to know about projected gradient descent and have a question. My understanding is that when you have constrained optimization problem, you use the duality to solve an easier dual problem, which also gives an answer to the original problem. Is the projected gradient descent just another method for solving constrained optimization problems? If so, when do people use the projected gradient descent instead of duality and vice versa?

Thanks,

I recently got to know about projected gradient descent and have a question. My understanding is that when you have constrained optimization problem, you use the duality to solve an easier dual problem, which also gives an answer to the original problem. Is the projected gradient descent just another method for solving constrained optimization problems? If so, when do people use the projected gradient descent instead of duality and vice versa?

Thanks,

I recently got to know about projected gradient descent and have a question. My understanding is that when you have constrained optimization problem, you use the duality to solve an easier dual problem, which also gives an answer to the original problem. Is the projected gradient descent just another method for solving constrained optimization problems? If so, when do people use the projected gradient descent instead of duality and vice versa?

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