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The paper describes a software package called LaGO for solving nonconvex mixed integer nonlinear programs (MINLPs). The main component of LaGO is a convex relaxation which is used for generating solution candidates and computing lower bounds of the optimal value. The relaxation is generated by reformulating the given MINLP as a block-separable problem, and(More)
e-mail: ivo@mathematik.hu-berlin.de Abstract. The purpose of this paper is threefold. First we propose splitting schemes for reformulating non-separable problems as block-separable problems. Second we show that the Lagrangian dual of a block-separable mixed-integer all-quadratic program (MIQQP) can be formulated as an eigenvalue optimization problem keeping(More)
This paper presents a smoothing heuristic for an NP-hard combinatorial problem. Starting with a convex Lagrangian relaxation, a pathfollowing method is applied to obtain good solutions while gradually transforming the relaxed problem into the original problem formulated with an exact penalty function. Starting points are drawn using different sampling(More)
The paper examines the applicability of mathematical programming methods to the simultaneous optimization of the structure and the operational parameters of a combined-cycle-based cogeneration plant. The optimization problem is formulated as a non-convex mixed-integer nonlinear problem (MINLP) and solved by the MINLP solver LaGO. The algorithm generates a(More)
min x FI(x,ξ) := ∑ i∈I pi f (xi,ξi) s.t. gt(n)(x 1, . . . ,xn,ζn) ≤ 0, xn ∈ Xt(n), n ∈ N(I) f (x,ξ), gt(x,ξ) convex in x, Xt convex, t = 1, . . . ,T Notation ξi i ∈ I scenarios of stoch. process ξ ξn := ξi,t(n) ζn := (ξ1, . . . ,ξn) xi i ∈ I decision vector for scenario i xn := xi,t(n) pi i ∈ I scenario probabilities N(I) nodes of scenario tree defined by(More)