# Dual Problem

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

Linear Programming - Duality
... 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 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 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 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 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)