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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)

We present a Branch and Cut algorithm of the software package LaGO to solve nonconvex mixed-integer nonlinear programs (MINLPs). A linear outer approximation is constructed from a convex relaxation of the problem. Since we do not require an algebraic representation of the problem, reformulation techniques for the construction of the convex relaxation cannot… (More)

The purpose of this paper is threefold. First we propose splitting schemes for re-formulating 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 the block-separable structure. Finally we… (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)

scenario probabilities N(I) nodes of scenario tree defined by scenarios in I t(n) timestage of node n T number of timestages Task: For scenarios I with tree N(I), find scenarios J ⊂ I and probabilities p J j , j ∈ J, such that |val(MSP[J]) − val(MSP[I])| and |J| are small. 1.: val(MSP[J]) ≫ val(MSP[J ′ ]) (∆ 1 ≫ 0) min x ∑ j∈J ∑ j ′ ∈J ′ : j(j ′)= j p J ′ j… (More)

- Ivo Nowak
- 1998

In this paper we compare two methods for estimating a global minimizer of an indeenite quadratic form over a simplex. The rst method is based on the enumeration of local minimizers of a so-called control polytope. The second method is based on an approximation of the convex envelope using semideenite programming. In order to test the algorithms a method for… (More)

- Ivo Nowak
- 2016

Traditional decomposition based branch-and-bound algorithms, like branch-and-price, can be very ecient if the duality gap is not too large. However, if this is not the case, the branch-and-bound tree may grow rapidly, preventing the method to nd a good solution. In this paper, we present a new decompositon algorithm, called ADGO (Alternating Direction… (More)