### Some articles on *problem, dual problem, dual, dual problems, problems*:

Linear Programming - Duality

... Every linear programming

... Every linear programming

**problem**, referred to as a primal**problem**, can be converted into a**dual problem**, which provides an upper bound to the optimal value of the primal**problem**... In matrix form, we can express the primal**problem**as Maximize cTx subject to Ax ≤ b, x ≥ 0 with the corresponding symmetric**dual problem**, Minimize bTy ... formulation is Maximize cTx subject to Ax ≤ b with the corresponding asymmetric**dual problem**, Minimize bTy subject to ATy = c, y ≥ 0 ...Duality (optimization) - The Non-linear Case - Convex Problems

... For a convex minimization

... For a convex minimization

**problem**with inequality constraints, the Lagrangian**dual problem**is where the objective function is the Lagrange**dual**function ... The**problem**is called the Wolfe**dual problem**... This**problem**may be difficult to deal with computationally, because the objective function is not concave in the joint variables ...Constraint Satisfaction

... The

**Dual Problem**... The

**dual problem**is a reformulation of a constraint satisfaction**problem**expressing each constraint of the original**problem**as a variable ...**Dual problems**only contain binary constraints, and are therefore solvable by algorithms tailored for such**problems**... The join graphs and join trees of a constraint satisfaction**problem**are graphs representing its**dual problem**or a**problem**obtained from the**dual problem**removing some redundant constraints ...Constraint Satisfaction

... The

**Dual Problem**- The**Dual Problem**... The

**dual problem**of a constraint satisfaction**problem**contains a variable for each constraint of the original**problem**... so to enforce a sort of equivalence to the original**problem**... In particular, the domain of a variable of the**dual problem**contains one element for each tuple satisfying the corresponding original constraint ...Duality (optimization) - The Linear Case - Relationship Between The Primal Problem and The

... In the linear case, in the primal

**Dual Problem**... In the linear case, in the primal

**problem**, from each sub-optimal point that satisfies all the constraints, there is a direction or subspace of directions ... In the**dual problem**, the**dual**vector multiplies the constants that determine the positions of the constraints in the primal ... Varying the**dual**vector in the**dual problem**is equivalent to revising the upper bounds in the primal**problem**...### Famous quotes containing the words problem and/or dual:

“The *problem* is simply this: no one can feel like CEO of his or her life in the presence of the people who toilet trained her and spanked him when he was naughty. We may have become Masters of the Universe, accustomed to giving life and taking it away, casually ordering people into battle or out of their jobs . . . and yet we may still dirty our diapers at the sound of our mommy’s whimper or our daddy’s growl.”

—Frank Pittman (20th century)

“Thee for my recitative,

Thee in the driving storm even as now, the snow, the winter-day

declining,

Thee in thy panoply, thy measur’d *dual* throbbing and thy beat

convulsive,

Thy black cylindric body, golden brass and silvery steel,”

—Walt Whitman (1819–1892)

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