11 Bibliographic notesΒΆ

The material on linear optimization is very basic, and can be found in any textbook. For further details, we suggest a few standard references [Chv83], [BT97] and [PS98], which all cover much more that discussed here. [NW06] gives a more modern treatment of both theory and algorithmic aspects of linear optimization.

Material on conic quadratic optimization is based on the paper [LVBL98] and the books [BenTalN01], [BV04]. The papers [AG03], [ART03] contain additional theoretical and algorithmic aspects.

For more theory behind the power cone and the exponential cone we recommend the thesis [Cha09].

Much of the material about semidefinite optimization is based on the paper [VB96] and the books [BenTalN01], [BKVH07]. The section on optimization over nonnegative polynomials is based on [Nes99], [Hac03]. We refer to [LR05] for a comprehensive survey on semidefinite optimization and relaxations in combinatorial optimization.

The chapter on conic duality follows the exposition in [GartnerM12]

Mixed-integer optimization is based on the books [NW88], [Wil93]. Modeling of piecewise linear functions is described in the survey paper [VAN10].