# Sebastian SagerOtto-von-Guericke-Universität Magdeburg | OvGU · Institute of Mathematical Optimization (IMO)

Sebastian Sager

Prof. Dr.

## About

116

Publications

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Introduction

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October 2008 - March 2012

## Publications

Publications (116)

Time transformation is a ubiquitous tool in theoretical sciences, especially in physics. It can also be used to transform switched optimal control problems into control problems with a fixed switching order and purely continuous decisions. This approach is known either as enhanced time transformation, time-scaling, or switching time optimization (S...

Complex dynamic systems are typically either modeled using expert knowledge in the form of differential equations, or via data-driven universal approximation models such as artificial neural networks (ANN). While the first approach has advantages with respect to interpretability, transparency, data-efficiency, and extrapolation, the second approach...

Mixed-integer optimal control problems arise in many practical applications combining nonlinear, dynamic, and combinatorial features. To cope with the resulting complexity, several approaches have been suggested in the past. Some of them rely on solving a reformulated and relaxed control problem, referred to as partial outer convexification. Inspir...

Purpose
Infections due to severe neutropenia are the most common therapy-associated causes of mortality in patients with acute myeloid leukemia (AML). New strategies to lessen the severity and duration of neutropenia are needed.
Methods
Cytarabine is commonly used for AML consolidation therapy; we compared high- and intermediate-dose cytarabine ad...

In the treatment of childhood acute lymphoblastic leukemia (ALL), current protocols combine initial high-dose multiagent chemotherapy with prolonged oral therapy with 6-mercaptopurine (6MP) and low-dose methotrexate (MTX) maintenance therapy. Decades of research on ALL treatment have resulted in survival rates of approximately 90%. However, dose-re...

For the fast approximate solution of Mixed-Integer Non-Linear Programs (MINLPs) arising in the context of Mixed-Integer Optimal Control Problems (MIOCPs) a decomposition algorithm exists that solves a sequence of three comparatively less hard subproblems to determine an approximate MINLP solution. In this work, we propose a problem formulation for...

Combinatorial integral approximation and binary trust-region steepest descent are two approaches for the solution of optimal control problems with discrete (binary in the latter case) control inputs. While the former method approximates solutions of a continuous relaxation with discrete controls, the latter produces a sequence of discrete and objec...

Mixed-integer optimal control problems governed by PDEs (MIPDECOs) are powerful mod-eling tools but also challenging in terms of theory and computation. We propose a highly efficient state elimination approach for MIPDECOs that are governed by PDEs that have the structure of an abstract ODE in function space. This allows us to avoid repeated calcul...

We present a trust-region steepest descent method for dynamic optimal control problems with binary-valued integrable control functions. Our method interprets the control function as an indicator function of a measurable set and makes set-valued adjustments derived from the sublevel sets of a topological gradient function. By combining this type of...

Using partial outer convexification, we can reformulate MINLPs constrained by ODEs or PDEs such that all integer control variables are binaries. We can obtain the canonical continuous relaxation of such problems by replacing the binary control variables with [0, 1]-valued ones. The relaxation is generally easier to solve. The two-step approach of c...

We propose a new method for the classification task of distinguishing atrial fibrillation (AFib) from regular atrial tachycardias including atrial flutter (AFlu) based on a surface electrocardiogram (ECG). Recently, many approaches for an automatic classification of cardiac arrhythmia were proposed and to our knowledge none of them can distinguish...

A promising treatment for congestive heart failure is the implementation of a left ventricular assist device (LVAD) that works as a mechanical pump. Modern LVADs work with adjustable constant rotor speed and provide therefore continuous blood flow; however, recently undertaken efforts try to mimic pulsatile blood flow by oscillating the pump speed....

The combinatorial integral approximation (CIA) decomposition suggests solving mixed-integer optimal control problems by solving one continuous nonlinear control problem and one mixed-integer linear program (MILP). Unrealistic frequent switching can be avoided by adding a constraint on the total variation to the MILP. Within this work, we present a...

This study considers the problem of computing a non-causal minimum-fuel energy management strategy for a hybrid electric vehicle on a given driving cycle. Specifically, we address the multiphase mixed-integer nonlinear optimal control problem that arises when the optimal gear choice, torque split and engine on/off controls are sought in off-line ev...

Tailored Mixed-Integer Optimal Control policies for real-world applications usually have to avoid very short successive changes of the active integer control. Minimum dwell time (MDT) constraints express this requirement and can be included into the combinatorial integral approximation decomposition, which solves mixed-integer optimal control probl...

Objective:
Neutropenia is an adverse event commonly arising during intensive chemotherapy of acute myeloid leukemia (AML). It is often associated with infectious complications. Mathematical modeling, simulation, and optimization of the treatment process would be a valuable tool to support clinical decision making, potentially resulting in less sev...

Polycythemia vera (PV) is a slow-growing type of blood cancer, where the production of red blood cells (RBCs) increase considerably. The principal treatment for targeting the symptoms of PV is bloodletting (phlebotomy) at regular intervals based on data derived from blood counts and physician assessments based on experience. Model-based decision su...

Background
Catheter ablation of right ventricular outflow tract ventricular arrhythmias from above the pulmonary valve is being increasingly reported.
Objective
The purpose of this study was to systematically analyze the spatial relationship between the pulmonary trunk and the left coronaries.
Methods
Contrast-enhanced computed tomographic scans...

Acute lymphoblastic leukemia is the most common malignancy in childhood. Successful treatment requires initial high-intensity chemotherapy, followed by low-intensity oral maintenance therapy with oral 6-mercaptopurine (6MP) and methotrexate (MTX) until 2–3 years after disease onset. However, intra- and inter-individual variability in the pharmacoki...

Application of Model Predictive Control (MPC) for nonlinear switched systems often leads via discretization to Mixed-Integer Non-Linear Programs (MINLPs), which in a real-time setting can be solved approximately using a dedicated decomposition approach. One stage within this approach is the solution of a so-called Combinatorial Integral Approximati...

Acute lymphoblastic leukemia is the most common malignancy in childhood. Successful treatment requires initial high-intensity chemotherapy, followed by low-intensity oral maintenance therapy with oral 6-mercaptopurine (6MP) and methotrexate (MTX) until 2-3 years after disease onset. However, intra- and interindividual variability in the pharmacokin...

Neutropenia is an adverse event commonly arising during intensive chemotherapy of acute myeloid leukemia (AML). It is often associated with infectious complications. Mathematical modeling, simulation, and optimization of the treatment process would be a valuable tool to support clinical decision making, potentially resulting in less severe side eff...

We investigate the personalisation and prediction accuracy of mathematical models for white blood cell (WBC) count dynamics during consolidation treatment using intermediate or high-dose cytarabine (Ara-C) in acute myeloid leukaemia (AML). Ara-C is the clinically most relevant cytotoxic agent for AML treatment. We extend a mathematical model of mye...

In this paper we present a numerical scheme for stochastic differential equations based upon the Wiener chaos expansion. The approximation of a square integrable stochastic differential equation is obtained by cutting off the infinite chaos expansion in chaos order and in number of basis elements. We derive an explicit upper bound for the $L^2$ app...

In this paper we present a numerical scheme for stochastic differential equations based upon the Wiener chaos expansion. The approximation of a square integrable stochastic differential equation is obtained by cutting off the infinite chaos expansion in chaos order and in number of basis elements. We derive an explicit upper bound for the ${L^{2}}$...

We analyze the maximal output power that can be obtained from a vibration energy harvester. While recent work focused on the use of mechanical nonlinearities and on determining the optimal resistive load at steady-state operation of the transducers to increase extractable power, we propose an optimal control approach. We consider the open-circuit s...

Acute lymphoblastic leukemia is the most common malignancy in childhood and requires prolonged oral maintenance chemotherapy to prevent disease relapse after remission induction with intensive intravenous chemotherapy. In maintenance therapy, drug doses of 6-mercaptopurine (6-MP) and methotrexate (MTX) are adjusted to achieve sustained antileukemic...

Optimal control problems with mixed integer control functions and logical implications, such as a state-dependent restriction on when a control can be chosen (so-called indicator or vanishing constraints) frequently arise in practice. A prominent example is the optimal cruise control of a truck. As every driver knows, admissible gear choices critic...

We investigate the personalisation and prediction accuracy of mathematical models for white blood cell (WBC) count dynamics during consolidation treatment using intermediate or high-dose cytarabine (Ara-C) in acute myeloid leukemia (AML). Ara-C is the clinically most relevant cytotoxic agent for AML treatment.
We extend the gold-standard model of m...

The regeneration of red blood cells (RBCs) after blood loss is an individual complex process. We present a novel simple compartment model which is able to capture the most important features and can be personalized using parameter estimation. We compare predictions of the proposed and personalized model to a more sophisticated state-of-the-art mode...

This work is devoted to demonstration of the mathematical analysis on maximizing the output power harvested from vibration energy harvester under a single sinusoidal input with time-dependent amplitude or drive frequency. While most of recent works have investigated the use of mechanical nonlinearities to increase extractable power, or determining...

In this paper we investigate a robust optimization framework for controlling energy storage devices in power networks with high share of fluctuating renewable energy sources. Our approach relies on the industry-standard DC power flow approximation, together with a multi-stage model that incorporates renewable uncertainty and an approximation of bat...

High voltage transmission networks play a crucial role in the ongoing transformation from centralized power generation in conventional power plants to decentralized generation from renewable energy sources (RES). The rapid expansion of RES requires a structural rearrangement of the entire power system to ensure the current level of supply security....

Nonlinear model predictive control has been established as a powerful methodology to provide feedback for dynamic processes over the last decades. In practice it is usually combined with parameter and state estimation techniques, which allows to cope with uncertainty on many levels. To reduce the uncertainty it has also been suggested to include op...

The enormous progress made in computational cardiac electrophysiology during the past decades has resulted in a diverse range of models and numerical methods. In general, researchers have elaborated highly complex and detailed simulators on the cell and tissue level. In contrast, there has been a lack of simplified whole-heart models that study spe...

Mathematical models are essential for simulation-driven decision support for clinical doctors. For an estimation of parameters for patient specific models, values such as the number of certain blood cells need to be measured. In this paper we focus on leukopenia, a clinically important side effect arising from the treatment of leukemia with chemoth...

Leukopenia is one of the most harmful side effects during chemotherapy treatment, since leukocytes (L) are crucial in protecting patients against bacteria and fungi. A personalized mathematical model of dynamics of L would allow a glimpse into the future and the initiation of tailored countermeasures. We propose such a mathematical model and calibr...

We present a quasi-Newton sequential quadratic programming (SQP) algorithm for nonlinear programs in which the Hessian of the Lagrangian function is block-diagonal. Problems with this characteristic frequently arise in the context of optimal control; for example, when a direct multiple shooting parametrization is used. In this article, we describe...

Quadratic programming problems (QPs) that arise from dynamic optimization problems typically exhibit a very particular structure. We address the ubiquitous case where these QPs are strictly convex and propose a dual Newton strategy that exploits the block-bandedness similarly to an interior-point method. Still, the proposed method features warmstar...

We compare different approaches of optimization under uncertainty in the context of pricing strategies for conspicuous consumption products in recession periods of uncertain duration and strength. We consider robust worst-case ideas and how the concepts of Value at Risk (VaR) and Conditional Value at Risk (CVaR) can be incorporated efficiently. The...

Background
The discrimination of atrial flutter (AFlu) and atrial fibrillation (AFib) can be made difficult by an irregular ventricular response due to complex conduction phenomena within the atrioventricular (AV) node, known as multilevel AV block. We tested the hypothesis that a mathematical algorithm might be suitable to discriminate between bot...

We present a control problem for an electrical vehicle. Its motor can be operated in two discrete modes, leading either to acceleration and energy consumption, or to a recharging of the battery. Mathematically, this leads to a mixed-integer optimal control problem (MIOCP) with a discrete feasible set for the controls taking into account the electri...

The control of autonomous vehicles
is a challenging task that requires advanced control schemes. Nonlinear Model Predictive Control (NMPC) and Moving Horizon Estimation (MHE) are optimization-based control and estimation techniques that are able to deal with highly nonlinear, constrained, unstable and fast dynamic systems. In this chapter, these te...

We introduce a novel generic methodology to solve continuous finite-horizon stochastic optimal control problems (SOCPs). We treat controlled stochastic differential equations (SDEs) within the Wiener chaos framework by utilizing Malliavin calculus and developing innovative ideas to preserve the feedback character of optimal Markov decision rules.
T...

We are interested in the optimal control of sewage networks. It is of high public interest to minimize the overflow of sewage onto the streets and to the natural environment that may occur during periods of heavy rain. The assumption of linear flow in a discrete time setting has proven to be adequate for the practical control of larger systems. How...

Logical implications appear in a number of important mixed-integer nonlinear optimal control problems (MIOCPs). Mathematical optimization offers a variety of different formulations that are equivalent for boolean variables, but result in different relaxations. In this article we give an overview over a variety of different modeling approaches, incl...

We address the problem of real-time obstacle avoidance on low-friction road surfaces using spatial Nonlinear Model Predictive Control (NMPC). We use a nonlinear four-wheel vehicle dynamics model that includes load transfer. To overcome the computational difficulties we propose to use the ACADO Code Generation tool which generates NMPC algorithms ba...

We present a novel numerical method for nonlinear model-predictive control of heavy-duty trucks. This method realizes a predictive online cruise controller, and includes the opportunity for multiple predictive gear choices. The combination of nonlinear dynamics, constraints, and objective with the hybrid nature of the gear choice makes for a challe...

We propose a novel and generic methodology for solving continuous finite-horizon stochastic optimal control problems. We develop innovative ideas for approximating controlled stochastic differential equations within the Wiener chaos framework and expand them to reformulate stochastic optimal control problems directly into deterministic ones. Within...

In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems arise, e.g., from the outer convexification of integer control decisions. We treat this optimal control problem class using the direct multiple shooting method to discretize the optimal control problem. The resul...

The present invention relates to a system for automatically distinguishing atrial flutter from atrial fibrillation based on a sequence of R-R-intervals of ECG data. The system of the invention comprises means adapted to calculate or simulate an R-R-pattern from a model which is based on a periodic or almost periodic signal representing peaks of an...

Combinatiorial and logic constraints arising in a number of challenging optimization applications can be formulated as vanishing constraints. Quadratic programs with vanishing constraints (QPVCs) then arise as subproblems during the numerical solution of such problems using algorithms of the sequential quadratic programming type. QPVCs are nonconve...

Numerical algorithm developers need standardized test instances for empirical studies and proofs of concept. There are several libraries available for finitedimensional optimization, such as the netlib or the miplib. However, for mixed-integer optimal control problems (MIOCP) this is not yet the case. One explanation for this is the fact that no do...

We consider integer-restricted optimal control of systems governed by
abstract semilinear evolution equations. This includes the problem of optimal
control design for certain distributed parameter systems endowed with multiple
actuators, where the task is to minimize costs associated with the dynamics of
the system by choosing, for each instant in...

In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems typically arise from the convexifica- tion of integer control decisions. We treat this problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear pr...

Over the last years, psychological research has increasingly used computer-supported tests, especially in the analysis of complex human decision making and problem solving. The approach is to use computer-based test scenarios and to evaluate the performance of participants and correlate it to certain attributes, such as the participant's capacity t...

We are interested in the optimal control of dynamic processes that can be described by Differential Algebraic Equations (DAEs) and that include integer restrictions on some or all of the control functions. We assume the DAE system to be of index 1. In our study we consider necessary conditions of optimality for this specific case of a hybrid system...

We are interested in methods to solve mixed-integer nonlinear optimal control problems constrained by ordinary differential equations and combinatorial constraints on some of the control functions. To solve these problems we use a first discretize, then optimize approach to get a specially structured mixed-integer nonlinear program (MINLP). We deco...

Optimum experimental design (OED) problems are optimization problems in which an experimental setting and decisions on when to measure–the so-called sampling design–are to be determined such that a follow-up parameter estimation yields accurate results for model parameters. In this paper we use the interpretation of OED as optimal control problems...

Quadratic programs obtained for optimal control problems of dynamic or discrete-time processes usually involve highly block
structured Hessian and constraints matrices, to be exploited by efficient numerical methods. In interior point methods, this
is elegantly achieved by the widespread availability of advanced sparse symmetric indefinite factoriz...

In certain applications of PDE constrained optimization one would like to base an optimization method on an already existing contractive method (solver) for the forward problem. The forward problem consists of finding a feasible point with some parts of the variables (e.g., design variables) held fixed. This approach often leads to so-called simult...

We derive optimal pricing strategies for conspicuous consumption products in periods of recession. To that end, we formulate and investigate a two-stage economic optimal control problem that takes uncertainty of the recession period length and delay effects of the pricing strategy into account.
This non-standard optimal control problem is difficult...

We present a problem class of mixed-integer nonlinear programs (MINLPs) with nonconvex continuous relaxations which stem from economic test scenarios that are used in the analysis of human complex problem solving. In a round-based scenario participants hold an executive function. A posteriori a performance indicator is calculated and correlated to...

We are interested in structures and efficient methods for mixed-integer nonlinear programs (MINLP) that arise from a first discretize, then optimize approach to time-dependent mixed-integer optimal control problems (MIOCPs). In this study we focus on combinatorial constraints,
in particular on restrictions on the number of switches on a fixed time...

In this article, four different mathematical models of chemotherapy from the literature are investigated with respect to optimal control of drug treatment schedules. The various models are based on two different sets of ordinary differential equations and contain either chemotherapy, immunotherapy, anti-angiogenic therapy or combinations of these....

We present a problem class of mixed-integer nonlinear programs (MINLPs) with nonconvex continuous relaxations which stem from economic test scenarios that are used in the analysis of human complex problem solving. In a round-based scenario participants hold an executive function. A posteriori a performance indicator is calculated and correlated to...

In practical optimal control problems both integer control variables and multiple objectives can be present. The current paper proposes a generic and efficient solution strategy for these multiple objective mixed-integer optimal control problems (MO-MIOCPs) based on deterministic approaches. Hereto, alternative scalar multiple objective optimisatio...

We extend recent work on nonlinear optimal control problems with integer restrictions on some of the control functions (mixed-integer
optimal control problems, MIOCP). We improve a theorem (Sager etal. in Math Program 118(1): 109–149, 2009) that states that
the solution of a relaxed and convexified problem can be approximated with arbitrary precisi...

We present a numerical method and results for a recently published benchmark problem (Optim. Contr. Appl. Met. 2005; 26:1–18; Optim. Contr. Appl. Met. 2006; 27(3):169–182) in mixed-integer optimal control. The problem has its origin in automobile test-driving and involves discrete controls for the choice of gears. Our approach is based on a convexi...