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Weak duality
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<p>In <a href="/facts/Applied_mathematics/qyqklXXm">applied mathematics</a>, weak duality is a concept in <a href="/facts/Optimization/oRn8Iv5I">optimization</a> which states that the <a href="/facts/Duality_gap/xwCQ15DL">duality gap</a> is always greater than or equal to 0. This means that for any minimization problem, called the <i>primal problem</i>, the solution to the primal problem is always greater than or equal to the solution to the <a href="/facts/Duality_(optimization)/lXqeKfnK">dual maximization problem</a>.: 225 Alternatively, the solution to a primal maximization problem is always less than or equal to the solution to the dual minimization problem. So, in short: weak duality states that any solution feasible for the dual problem is an upper bound to the solution of the primal problem. </p><p>Weak duality is in contrast to <a href="/facts/Strong_duality/NtpAxpqj">strong duality</a>, which states that the primal optimal objective and the dual optimal objective are <i>equal</i>. Strong duality only holds in certain cases. </p>