Books > Science & Mathematics > Mathematics > Optimization
|
Buy Now
The Many Faces of Degeneracy in Conic Optimization (Paperback)
Loot Price: R1,913
Discovery Miles 19 130
|
|
The Many Faces of Degeneracy in Conic Optimization (Paperback)
Series: Foundations and Trends in Optimization
Expected to ship within 10 - 15 working days
|
Slater's condition - existence of a strictly feasible solution - is
a common assumption in conic optimization. Without strict
feasibility, first-order optimality conditions may be meaningless,
the dual problem may yield little information about the primal, and
small changes in the data may render the problem infeasible. Hence,
failure of strict feasibility can negatively impact off-the-shelf
numerical methods, such as primal-dual interior point methods, in
particular. New optimization modeling techniques and convex
relaxations for hard nonconvex problems have shown that the loss of
strict feasibility is a more pronounced phenomenon than has
previously been realized. The Many Faces of Degeneracy in Conic
Optimization describes various reasons for the loss of strict
feasibility, whether due to poor modeling choices or (more
interestingly) rich underlying structure, and discusses ways to
cope with it and, in many pronounced cases, how to use it as an
advantage. In large part, it emphasizes the facial reduction
preprocessing technique due to its mathematical elegance, geometric
transparency, and computational potential. The Many Faces of
Degeneracy in Conic Optimization is divided into two parts. Part I
presents the necessary theoretical grounding in conic optimization,
including basic optimality and duality theory, connections of
Slater's condition to the distance to infeasibility and sensitivity
theory, the facial reduction procedure, and the singularity degree.
Part II focuses on illustrative examples and applications,
including matrix completion problems (semidefinite, low-rank, and
Euclidean distance), relaxations of hard combinatorial problems
(quadratic assignment and max-cut), and sum of squares relaxations
of polynomial optimization problems.
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
|
|
Email address subscribed successfully.
A activation email has been sent to you.
Please click the link in that email to activate your subscription.