Open Access
Introduction to Mixed Integer Nonlinear Programming
Luca Mencarelli
- 01 Jan 2014
1
About: The article was published on 01 Jan 2014. and is currently open access. The article focuses on the topics: Branch and price & Integer programming.
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Citations
A trajectory-based method for mixed integer nonlinear programming problems
TL;DR: It is shown that the optimal value obtained by the proposed method is at least as good as the minimizer predicted by a recent definition of a mixed integer local minimizer.
2
References
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Interior-Point Polynomial Algorithms in Convex Programming
Yurii Nesterov,Arkadii Nemirovskii +1 more
- 01 Jan 1987
TL;DR: This book describes the first unified theory of polynomial-time interior-point methods, and describes several of the new algorithms described, e.g., the projective method, which have been implemented, tested on "real world" problems, and found to be extremely efficient in practice.
A new polynomial-time algorithm for linear programming
TL;DR: It is proved that given a polytopeP and a strictly interior point a εP, there is a projective transformation of the space that mapsP, a toP′, a′ having the following property: the ratio of the radius of the smallest sphere with center a′, containingP′ to theradius of the largest sphere withCenter a′ contained inP′ isO(n).
5K
A new polynomial-time algorithm for linear programming
Narendra Karmarkar
- 01 Dec 1984
TL;DR: The algorithm consists of repeated application of such projective transformations each followed by optimization over an inscribed sphere to create a sequence of points which converges to the optimal solution in polynomial-time.
Generalized Benders decomposition
TL;DR: In this paper, the extremal value of the linear program as a function of the parameterizing vector and the set of values of the parametric vector for which the program is feasible were derived using linear programming duality theory.
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