Afhalen na 1 uur in een winkel met voorraad
Gratis thuislevering in België vanaf € 30
Ruim aanbod met 7 miljoen producten

Afhalen na 1 uur in een winkel met voorraad
Gratis thuislevering in België vanaf € 30
Ruim aanbod met 7 miljoen producten

Winkels

Verlanglijstje

Winkels

Verlanglijstje

Zoeken

Volg ons op

Wist je dat er in Vlaanderen voor iedereen een Standaard Boekhandel is binnen een straal van 7 km?

Zoek een winkel

€ 108,95

+ 217 punten

Levering 2 à 3 weken

Eenvoudig bestellen

Veilig betalen

Gratis thuislevering vanaf € 30 (via bpost)

Gratis levering in je Standaard Boekhandel

Omschrijving

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.