This can be formulated by an SDP . We handle the inequality constraints by augmenting the variable matrix and introducing slack variables, for example
12.
The method of Lagrange multipliers is generalized by the Karush Kuhn Tucker conditions, which can also take into account inequality constraints of the form.
13.
The second and third lines define two constraints, the first of which is an inequality constraint and the second of which is an equality constraint.
14.
Note that the second inequality constraint defines the debt limit of the maximization problem and \ eta stands for the debt limit that the agent faces.
15.
In an optimization problem, a "'slack variable "'is a variable that is added to an inequality constraint to transform it to an equality.
16.
A common partial solution to the ill-posedness problem consists of imposing an additional inequality constraint that bounds the norm of the individual rank-1 terms by some constant.
17.
With inequality constraints, the problem can be characterized in terms of the Geometric Optimality conditions, Fritz John conditions and Karush Kuhn Tucker conditions, in which simple problems may be solvable.
18.
:A linear programming problem is to minimize ( maximize ) a linear " objective function " in one or more variables, with the variables subject to linear equality or inequality constraints.
19.
Each search direction is calculated so that it does not intersect the boundary of any inequality constraint that is satisfied and that has a " small " residual at the beginning of the line search.
20.
Note that every equality constraint h ( x ) = 0 can be equivalently replaced by a pair of inequality constraints h ( x ) \ leq 0 and-h ( x ) \ leq 0.
