Martin Schmidt – Page 10 – Optimization Online

Penalty Alternating Direction Methods for Mixed-Integer Optimization: A New View on Feasibility Pumps

Published: 2016/04/07, Updated: 2017/03/22

Feasibility pumps are highly effective primal heuristics for mixed-integer linear and nonlinear optimization. However, despite their success in practice there are only few works considering their theoretical properties. We show that feasibility pumps can be seen as alternating direction methods applied to special reformulations of the original problem, inheriting the convergence theory of these methods. … Read more

A Distributed Interior-Point KKT Solver for Multistage Stochastic Optimization

Published: 2016/02/09, Updated: 2016/02/10

Hübner Jens

Martin Schmidt

Marc C. Steinbach

Finance and Economics, Parallel Algorithms, Stochastic Programming distributed computing, interior point methods, kkt systems, multistage stochastic programming, parallel computing

Multistage stochastic optimization leads to NLPs over scenario trees that become extremely large when many time stages or fine discretizations of the probability space are required. Interior-point methods are well suited for these problems if the arising huge, structured KKT systems can be solved efficiently, for instance, with a large scenario tree but a moderate … Read more

GasLib – A Library of Gas Network Instances

Published: 2015/11/25, Updated: 2017/11/18

(Mixed) Integer Nonlinear Programming, Applications - Science and Engineering gas transport, gaslib, mixed-integer nonlinear programming, networks, problem instances

The development of mathematical simulation and optimization models and algorithms for solving gas transport problems is an active field of research. In order to test and compare these models and algorithms, gas network instances together with demand data are needed. The goal of GasLib is to provide a set of publicly available gas network instances … Read more

Uniqueness of Market Equilibrium on a Network: A Peak-Load Pricing Approach

Published: 2015/08/25, Updated: 2017/03/14

Convex Optimization, Finance and Economics, Network Optimization networks, peak-load pricing, pricing, uniqueness

In this paper we establish conditions under which uniqueness of market equilibrium is obtained in a setup where prior to trading of electricity, transmission capacities between different market regions are fixed. In our setup, firms facing fluctuating demand decide on the size and location of production facilities. They make production decisions constrained by the invested … Read more

Transmission and Generation Investment in Electricity Markets: The Effects of Market Splitting and Network Fee Regimes

Published: 2015/03/04

(Mixed) Integer Nonlinear Programming, Finance and Economics, Network Optimization electricity markets, equilibrium models, mixed-integer nonlinear programming, multiobjective optimization, network expansion, transmission management

We propose an equilibrium model that allows to analyze the long-run impact of the regulatory environment on transmission line expansion by the regulator and investment in generation capacity by private firms in liberalized electricity markets. The model incorporates investment decisions of the transmission operator and private firms in expectation of an energy-only market and cost-based … Read more

Computational Optimization of Gas Compressor Stations: MINLP Models vs. Continuous Reformulations

Published: 2015/02/26

(Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Nonlinear Optimization continuous reformulations, discrete-continuous nonlinear optimization, gas compressor stations, gas networks, mixed-integer programming

When considering cost-optimal operation of gas transport networks, compressor stations play the most important role. Proper modeling of these stations leads to complicated mixed-integer nonlinear and nonconvex optimization problems. In this article, we give an isothermal and stationary description of compressor stations, state MINLP and GDP models for operating a single station, and discuss several … Read more

Solving Power-Constrained Gas Transportation Problems using an MIP-based Alternating Direction Method

Published: 2014/11/24, Updated: 2015/07/08

(Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Constrained Nonlinear Optimization alternating direction method, gas transport networks, heat power supply and demand, nonconvex mixed-integer nonlinear optimization, piecewise linear relaxations

We present a solution algorithm for problems from steady-state gas transport optimization. Due to nonlinear and nonconvex physics and engineering models as well as discrete controllability of active network devices, these problems lead to hard nonconvex mixed-integer nonlinear optimization models. The proposed method is based on mixed-integer linear techniques using piecewise linear relaxations of the … Read more

High Detail Stationary Optimization Models for Gas Networks: Validation and Results

Published: 2014/10/15, Updated: 2014/11/26

Martin Schmidt

Marc C. Steinbach

Bernhard M. Willert

Applications - Science and Engineering, Constrained Nonlinear Optimization, Systems governed by Differential Equations Optimization gas networks, high-detail modeling, sequential nlp solving, stationary operation

Due to strict regulatory rules in combination with complex nonlinear physics, major gas network operators in Germany and Europe face hard planning problems that call for optimization. In part 1 of this paper we have developed a suitable model hierarchy for that purpose. Here we consider the more practical aspects of modeling. We validate individual … Read more

An Interior-Point Method for Nonlinear Optimization Problems with Locatable and Separable Nonsmoothness

Published: 2014/04/29, Updated: 2014/10/23

Martin Schmidt

Applications - Science and Engineering, Constrained Nonlinear Optimization, Nonsmooth Optimization barrier methods, classification of optimization models, gas network optimization, interior point methods, line search methods, nonlinear and nonsmooth optimization

A lot of real-world optimization models comprise nonconvex and nonlinear as well as nonsmooth functions leading to very hard classes of optimization models. In this article a new interior-point method for the special but practically relevant class of optimization problems with locatable and separable nonsmooth aspects is presented. After motivating and formalizing the problems under … Read more

Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions

Published: 2012/11/30, Updated: 2013/11/17

(Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Systems governed by Differential Equations Optimization gas transport optimization, mixed-integer nonlinear programming, real-world instances

In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements … Read more