On a Dual Direct Cosine Simplex Type Algorithm and Its Computational Behavior
Algorithm 1
Dual cosine simplex method (DCSM).
Require: infeasible basis
While b i < 0
Step 1 (dual feasibility condition): let N is the index set of the nonbasic variables. The leaving variable, xi, is the basic variable having the maximum for minimization problem, where is the angle between the constraint i and the objective function. The tie is broken by choosing the most negative value in the right hand side.
Step 2 (dual optimality condition): given that xi is the leaving variable, the entering variable is the nonbasic variable aij < 0 that corresponds to The ties are broken arbitrary. If for all nonbasic variables, then the problem has no feasible solution.
