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Books > Science & Mathematics > Mathematics > Optimization
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The Projected Subgradient Algorithm in Convex Optimization (Paperback, 1st ed. 2020)
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The Projected Subgradient Algorithm in Convex Optimization (Paperback, 1st ed. 2020)
Series: SpringerBriefs in Optimization
Expected to ship within 10 - 15 working days
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This focused monograph presents a study of subgradient algorithms
for constrained minimization problems in a Hilbert space. The book
is of interest for experts in applications of optimization to
engineering and economics. The goal is to obtain a good approximate
solution of the problem in the presence of computational errors.
The discussion takes into consideration the fact that for every
algorithm its iteration consists of several steps and that
computational errors for different steps are different, in general.
The book is especially useful for the reader because it contains
solutions to a number of difficult and interesting problems in the
numerical optimization. The subgradient projection algorithm is one
of the most important tools in optimization theory and its
applications. An optimization problem is described by an objective
function and a set of feasible points. For this algorithm each
iteration consists of two steps. The first step requires a
calculation of a subgradient of the objective function; the second
requires a calculation of a projection on the feasible set. The
computational errors in each of these two steps are different. This
book shows that the algorithm discussed, generates a good
approximate solution, if all the computational errors are bounded
from above by a small positive constant. Moreover, if computational
errors for the two steps of the algorithm are known, one discovers
an approximate solution and how many iterations one needs for this.
In addition to their mathematical interest, the generalizations
considered in this book have a significant practical meaning.
General
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