Sphere Methods for LP
For solving an optimization problem in which an objective function z(x) is to be minimized subject to constraints, starting with an initial feasible solution, a method that works by generating a sequence of feasible solutions along which the objective value z(x) strictly decreases is known as a descent algorithm. Strict improvement in the objective value in each step is an appealing property, and hence descent algorithms are the most sought after.
If the original objective function is to be maximized instead, algorithms that maintain feasibility and improve the objective value (i.e., here, increasing its value) in every step are also referred to as descent algorithms.
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