Raftul cu initiativa Book Archive

Machine Theory

Bilevel Programming Problems: Theory, Algorithms and by Stephan Dempe, Vyacheslav Kalashnikov, Gerardo A.

By Stephan Dempe, Vyacheslav Kalashnikov, Gerardo A. Pérez-Valdés, Nataliya Kalashnykova

This e-book describes contemporary theoretical findings proper to bilevel programming commonly, and in mixed-integer bilevel programming specifically. It describes contemporary functions in strength difficulties, akin to the stochastic bilevel optimization techniques utilized in the ordinary gasoline undefined. New algorithms for fixing linear and mixed-integer bilevel programming difficulties are offered and explained.

Show description

Read or Download Bilevel Programming Problems: Theory, Algorithms and Applications to Energy Networks PDF

Best machine theory books

Digital and Discrete Geometry: Theory and Algorithms

This e-book offers complete insurance of the fashionable equipment for geometric difficulties within the computing sciences. It additionally covers concurrent themes in info sciences together with geometric processing, manifold studying, Google seek, cloud information, and R-tree for instant networks and BigData. the writer investigates electronic geometry and its similar optimistic equipment in discrete geometry, supplying distinctive equipment and algorithms.

Artificial Intelligence and Symbolic Computation: 12th International Conference, AISC 2014, Seville, Spain, December 11-13, 2014. Proceedings

This publication constitutes the refereed lawsuits of the twelfth foreign convention on man made Intelligence and Symbolic Computation, AISC 2014, held in Seville, Spain, in December 2014. The 15 complete papers offered including 2 invited papers have been conscientiously reviewed and chosen from 22 submissions.

Statistical Language and Speech Processing: Third International Conference, SLSP 2015, Budapest, Hungary, November 24-26, 2015, Proceedings

This booklet constitutes the refereed complaints of the 3rd foreign convention on Statistical Language and Speech Processing, SLSP 2015, held in Budapest, Hungary, in November 2015. The 26 complete papers provided including invited talks have been conscientiously reviewed and chosen from seventy one submissions.

Additional info for Bilevel Programming Problems: Theory, Algorithms and Applications to Energy Networks

Sample text

16) has a unique solution (r, γ ) and, hence, r equals the directional derivative y (x; d) of the solution function y(·) at x into direction d, see Bigelow and Shapiro [22]. 16) has a solution, this does not need to be true since this system is not suitable to the direction. 10). 16) equals (y (x; d), γ ) for some direction d is Ai d + Bi r ≤ 0 for i with Ai x + Bi y − ci = 0 and γi ≥ 0 for i with λi0 = 0. 12) is piecewise affine-linear. This implies that it is a Lipschitz continuous function, its directional derivative 1 d → y (x; d) = lim [y(x + td) − y(x)] t↓0 t is also Lipschitz continuous.

1 (Mersha and Dempe [227]). Consider the problem min −x − 2y x,y 2x − 3y ≥ −12 x + y ≤ 14 subject to and y ∈ Argmin {−y : −3x + y ≤ −3, 3x + y ≤ 30}. y © Springer-Verlag Berlin Heidelberg 2015 S. 1007/978-3-662-45827-3_2 21 22 2 Linear Bilevel Optimization Problem Fig. 1 The problem with upper level connecting constraints. The feasible set is depicted with bold lines. The point C is global optimal solution, point A is a local optimal solution Fig. 2 The problem when the upper level connecting constraints are shifted into the lower level problem.

20) yi = 0 ∀i ∈ I (y) b ∈ B 0 and the tangent cone TR (y) = {d : Ad = r, Br = 0, di ≥ 0, i ∈ I (y)\ I 0 (y), di = 0, i ∈ I 0 (y)} to the feasible set of this problem at the point y again relative to y only. e. the set of all linear combinations of elements in S with nonnegative coefficients. Let spanS denote the set of all linear combinations of elements in S. 22) where Ai denotes the ith column of the matrix A. 4 All non degenerated vertices of Ay = b, y ≥ 0 satisfy the full rank condition. This condition allows us now to establish equality between the cones above.

Download PDF sample

Rated 4.04 of 5 – based on 4 votes