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    Item type:Publication, Access status: with files ,
    Partially distributed outer approximation
    (Springer, 2021-04-17)
    Murray, Alexander
    ;
    Faulwasser, Timm
    ;
    Hagenmeyer, Veit
    ;
    Villanueva, Mario E.
    ;
    Houska, Boris
    This paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression.
    Publicationtype: Journal Article
    Scopus© Citations 1  10  28
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    Item type:Publication, Access status: without files ,
    A rigorous lower bound for the optimal value of convex optimization problems
    (Springer Science + Business Media B.V, 2004-01)
    Jansson, Christian
    In this paper, we consider the computation of a rigorous lower error bound for the optimal value of convex optimization problems. A discussion of large-scale problems, degenerate problems, and quadratic programming problems is included. It is allowed that parameters, which define the convex constraints and the convex objective functions, may be uncertain and may vary between given lower and upper bounds. The error bound is verified for the family of convex optimization problems which correspond to these uncertainties. It can be used to perform a rigorous sensitivity analysis in convex programming, provided the width of the uncertainties is not too large. Branch and bound algorithms can be made reliable by using such rigorous lower bounds.
    Publicationtype: Journal Article
      43
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    Item type:Publication, Access status: without files ,
    A branch and bound algorithm for bound constrained optimization problems without derivatives
    (Springer, 1995-10-01)
    Jansson, Christian
    ;
    Knüppel, Olaf
    In this paper, we give a new branch and bound algorithm for the global optimization problem with bound constraints. The algorithm is based on the use of inclusion functions. The bounds calculated for the global minimum value are proved to be correct, all rounding errors are rigorously estimated. Our scheme attempts to exclude most "uninteresting" parts of the search domain and concentrates on its "promising" subsets. This is done as fast as possible (by involving local descent methods), and uses little information as possible (no derivatives are required). Numerical results for many well-known problems as well as some comparisons with other methods are given. © 1995 Kluwer Academic Publishers.
    Publicationtype: Journal Article
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