Mixed-integer nonlinear optimization

P Belotti, C Kirches, S Leyffer, J Linderoth, J Luedtke… - Acta Numerica, 2013 - cambridge.org
Many optimal decision problems in scientific, engineering, and public sector applications
involve both discrete decisions and nonlinear system dynamics that affect the quality of the …

[图书][B] Disjunctive programming

E Balas - 2018 - books.google.com
Disjunctive Programming is a technique and a discipline initiated by the author in the early
1970's, which has become a central tool for solving nonconvex optimization problems like …

Polyhedral approximation in mixed-integer convex optimization

M Lubin, E Yamangil, R Bent, JP Vielma - Mathematical Programming, 2018 - Springer
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer
convex optimization possesses broad modeling power but has seen relatively few advances …

Submodularity in conic quadratic mixed 0–1 optimization

A Atamtürk, A Gómez - Operations Research, 2020 - pubsonline.informs.org
We describe strong convex valid inequalities for conic quadratic mixed 0–1 optimization.
These inequalities can be utilized for solving numerous practical nonlinear discrete …

[图书][B] Integer programming, lattice algorithms, and deterministic volume estimation

DN Dadush - 2012 - search.proquest.com
The main subject of this thesis is the development of new geometric tools and techniques for
solving classic problems within the geometry of numbers and convex geometry. At a high …

On minimal valid inequalities for mixed integer conic programs

F Kılınç-Karzan - Mathematics of Operations Research, 2016 - pubsonline.informs.org
We study disjunctive conic sets involving a general regular (closed, convex, full dimensional,
and pointed) cone 𝒦 such as the nonnegative orthant, the Lorentz cone, or the positive …

Intersection cuts for nonlinear integer programming: convexification techniques for structured sets

S Modaresi, MR Kılınç, JP Vielma - Mathematical Programming, 2016 - Springer
We study the generalization of split, k-branch split, and intersection cuts from mixed integer
linear programming to the realm of mixed integer nonlinear programming. Constructing such …

A conic representation of the convex hull of disjunctive sets and conic cuts for integer second order cone optimization

P Belotti, JC Góez, I Pólik, TK Ralphs… - Numerical Analysis and …, 2015 - Springer
We study the convex hull of the intersection of a convex set E and a disjunctive set. This
intersection is at the core of solution techniques for Mixed Integer Convex Optimization. We …

How to convexify the intersection of a second order cone and a nonconvex quadratic

S Burer, F Kılınç-Karzan - Mathematical Programming, 2017 - Springer
A recent series of papers has examined the extension of disjunctive-programming
techniques to mixed-integer second-order-cone programming. For example, it has been …

Split cuts and extended formulations for mixed integer conic quadratic programming

S Modaresi, MR Kılınç, JP Vielma - Operations Research Letters, 2015 - Elsevier
We study split cuts and extended formulations for Mixed Integer Conic Quadratic
Programming (MICQP) and their relation to Conic Mixed Integer Rounding (CMIR) cuts. We …