Alberto De Marchi

Publications

Preprints

Hybrid optimal control with mixed-integer Lagrangian methods

Nikitina, De Marchi, Gerdts. (2024)

[ abstract | pdf | bibtex ]

@misc{nikitina2024hybrid,
    author      = {Nikitina, Viktoriya and De~Marchi, Alberto and Gerdts, Matthias},
    title       = {Hybrid optimal control with mixed-integer {L}agrangian methods},
    year        = {2024},
    eprinttype  = {arxiv},
    eprint      = {2403.06842},
}

submitted to CDC 2024

Mixed-integer linearity in nonlinear optimization: a trust region approach

De Marchi. (2023)

[ abstract | pdf | bibtex | code ]

@misc{demarchi2023mixed,
    author      = {De~Marchi, Alberto},
    title       = {Mixed-integer linearity in nonlinear optimization: a trust region approach},
    year        = {2023},
    eprinttype  = {arxiv},
    eprint      = {2310.17285},
}

submitted to Optim Lett

Local properties and augmented Lagrangians in fully nonconvex composite optimization

De Marchi, Mehlitz. (2023)

[ abstract | pdf | bibtex ]

@misc{demarchi2023local,
    author      = {De~Marchi, Alberto and Mehlitz, Patrick},
    title       = {Local properties and augmented {L}agrangians in fully nonconvex composite optimization},
    year        = {2023},
    eprinttype  = {arxiv},
    eprint      = {2309.01980},
}

submitted to JNSAO

An interior proximal gradient method for nonconvex optimization

De Marchi, Themelis. (2022)

[ abstract | pdf | bibtex | code | poster ]

@misc{demarchi2022interior,
    author      = {De~Marchi, Alberto and Themelis, Andreas},
    title       = {An interior proximal gradient method for nonconvex optimization},
    year        = {2022},
    eprinttype  = {arxiv},
    eprint      = {2208.00799},
}

submitted to OJMO

Journal Articles

Implicit augmented Lagrangian and generalized optimization

De Marchi. (2023)

[ abstract | pdf | bibtex | code ]

@article{demarchi2024implicit,
    author      = {De~Marchi, Alberto},
    title       = {Implicit augmented {L}agrangian and generalized optimization},
    journal     = {Journal of Applied and Numerical Optimization},
    year        = {2024},
    pages       = {291--320},
    volume      = {6},
    number      = {2},
    doi         = {10.23952/jano.6.2024.2.08},
    eprinttype  = {arxiv},
    eprint      = {2302.00363},
}

Journal of Applied and Numerical Optimization 6, 291–320 (2024).

Relativistic Digital Twin: Bringing the IoT to the future

Sciullo, De Marchi, Trotta, Montori, Bononi, Di Felice. (2022)

[ abstract | pdf | bibtex | code ]

@article{sciullo2024relativistic,
    author      = {Sciullo, Luca and De~Marchi, Alberto and Trotta, Angelo and Montori, Federico and Bononi, Luciano and Di~Felice, Marco},
    title       = {Relativistic {D}igital {T}win: Bringing the {IoT} to the future},
    journal     = {Future Generation Computer Systems},
    year        = {2024},
    volume      = {153},
    pages       = {521--536},
    eprinttype  = {arxiv},
    eprint      = {2301.07390},
    doi         = {10.1016/j.future.2023.12.016},
}

Future Generation Computer Systems 153, 521–536 (2024).

Dynamic and nonlinear programming for trajectory planning

Britzelmeier, De Marchi, Richter. (2023)

[ abstract | pdf | bibtex ]

@article{britzelmeier2023dynamic,
    author      = {Britzelmeier, Andreas and De~Marchi, Alberto and Richter, Rebecca},
    title       = {Dynamic and nonlinear programming for trajectory planning},
    journal     = {IEEE Control Systems Letters},
    year        = {2023},
    volume      = {7},
    pages       = {2569--2574},
    issn        = {2475-1456},
    doi         = {10.1109/LCSYS.2023.3285746},
}

IEEE Control Systems Letters 7, 2569–2574 (2023).
62th IEEE Conference on Decision and Control (CDC), Dec 2023, Singapore.

Proximal gradient methods beyond monotony

De Marchi. (2022)

[ abstract | pdf | bibtex | code ]

@article{demarchi2023monotony,
    author      = {De~Marchi, Alberto},
    title       = {Proximal gradient methods beyond monotony},
    journal     = {Journal of Nonsmooth Analysis and Optimization},
    year        = {2023},
    volume      = {4},
    eprinttype  = {arxiv},
    eprint      = {2211.04827},
    doi         = {10.46298/jnsao-2023-10290},
}

Journal of Nonsmooth Analysis and Optimization 4, 10290 (2023).

Constrained composite optimization and augmented Lagrangian methods

De Marchi, Jia, Kanzow, Mehlitz. (2022)

[ abstract | pdf | bibtex | code ]

@article{demarchi2023constrained,
    author      = {De~Marchi, Alberto and Jia, Xiaoxi and Kanzow, Christian and Mehlitz, Patrick},
    title       = {Constrained composite optimization and augmented {L}agrangian methods},
    journal     = {Mathematical Programming},
    year        = {2023},
    month       = {9},
    volume      = {201},
    number      = {1},
    pages       = {863--896},
    eprinttype  = {arxiv},
    eprint      = {2203.05276},
    doi         = {10.1007/s10107-022-01922-4},
}

Mathematical Programming 201, 863–896 (2023).

A function approximation approach for parametric optimization

De Marchi, Dreves, Gerdts, Gottschalk, Rogovs. (2021)

[ abstract | pdf | bibtex ]

@article{demarchi2023function,
    author      = {De~Marchi, Alberto and Dreves, Axel and Gerdts, Matthias and Gottschalk, Simon and Rogovs, Sergejs},
    title       = {A function approximation approach for parametric optimization},
    journal     = {Journal of Optimization Theory and Applications},
    year        = {2023},
    month       = {1},
    volume      = {196},
    number      = {1},
    pages       = {56--77},
    doi         = {10.1007/s10957-022-02138-4},
}

Journal of Optimization Theory and Applications 196, 56–77 (2023).

Proximal gradient algorithms under local Lipschitz gradient continuity

De Marchi, Themelis. (2021)

[ abstract | pdf | bibtex | code ]

@article{demarchi2022proximal,
    author      = {De~Marchi, Alberto and Themelis, Andreas},
    title       = {Proximal gradient algorithms under local {L}ipschitz gradient continuity},
    journal     = {Journal of Optimization Theory and Applications},
    year        = {2022},
    pages       = {771--794},
    volume      = {194},
    number      = {3},
    eprinttype  = {arxiv},
    eprint      = {2112.13000},
    doi         = {10.1007/s10957-022-02048-5},
}

Journal of Optimization Theory and Applications 194, 771–794 (2022).

On a primal-dual Newton proximal method for convex quadratic programs

De Marchi. (2020)

[ abstract | pdf | bibtex | code ]

@article{demarchi2022qpdo,
    title       = {On a primal-dual {N}ewton proximal method for convex quadratic programs},
    author      = {De~Marchi, Alberto},
    journal     = {Computational Optimization and Applications},
    volume      = {81},
    number      = {2},
    pages       = {369--395},
    year        = {2022},
    month       = {3},
    doi         = {10.1007/s10589-021-00342-y},
}

Computational Optimization and Applications 81, 369–395 (2022).
🏆 COAP 2022 Best Paper Prize

On the mixed-integer linear-quadratic optimal control with switching cost

De Marchi. (2019)

[ abstract | pdf | bibtex | suppl ]

@article{demarchi2019mixed,
    author      = {De~Marchi, Alberto},
    title       = {On the mixed-integer linear-quadratic optimal control with switching cost},
    journal     = {IEEE Control Systems Letters},
    year        = {2019},
    month       = {10},
    volume      = {3},
    number      = {4},
    pages       = {990--995},
    issn        = {2475-1456},
    doi         = {10.1109/LCSYS.2019.2920425},
}

IEEE Control Systems Letters 3(4), 990–995 (2019).
58th IEEE Conference on Decision and Control (CDC), Dec 2019, Nice, FR.

Free finite horizon LQR: a bilevel perspective and its application to model predictive control

De Marchi, Gerdts. (2018)

[ abstract | pdf | bibtex ]

@article{demarchi2019free,
    author      = {De~Marchi, Alberto and Gerdts, Matthias},
    title       = {Free finite horizon {LQR}: a bilevel perspective and its application to model predictive control},
    journal     = {Automatica},
    year        = {2019},
    month       = {2},
    volume      = {100},
    pages       = {299--311},
    issn        = {0005-1098},
    doi         = {10.1016/j.automatica.2018.11.032},
}

Automatica 100, 299–311 (2019).

Conference Proceedings

Collision avoidance using iterative dynamic and nonlinear programming with adaptive grid refinements

Richter, De Marchi, Gerdts. (2023)

[ abstract | pdf | bibtex ]

@misc{richter2023collision,
    author      = {Richter, Rebecca and De~Marchi, Alberto and Gerdts, Matthias},
    title       = {Collision avoidance using iterative dynamic and nonlinear programming with adaptive grid refinements},
    year        = {2023},
    eprinttype  = {arxiv},
    eprint      = {2311.03148},
}

accepted for ECC 2024

Regularized interior point methods for constrained optimization and control

De Marchi. (2022)

[ abstract | pdf | bibtex | code ]

@article{demarchi2023regularized,
    author      = {De~Marchi, Alberto},
    title       = {Regularized interior point methods for constrained optimization and control},
    journal     = {IFAC-PapersOnLine},
    year        = {2023},
    volume      = {56},
    number      = {2},
    pages       = {1247--1252},
    eprinttype  = {arxiv},
    eprint      = {2210.15825},
    doi         = {10.1016/j.ifacol.2023.10.1747},
}

22nd IFAC World Congress, Jul 2023, Yokohama, JP.

Augmented Lagrangian methods as dynamical systems for constrained optimization

De Marchi. (2021)

[ abstract | pdf | bibtex | code ]

@inproceedings{demarchi2021augmented,
    author      = {De~Marchi, Alberto},
    title       = {Augmented {L}agrangian methods as dynamical systems for constrained optimization},
    year        = {2021},
    month       = {12},
    booktitle   = {2021 60th {IEEE} {C}onference on {D}ecision and {C}ontrol ({CDC})},
    doi         = {10.1109/CDC45484.2021.9683199},
}

60th IEEE Conference on Decision and Control (CDC), pp. 6533–6538, Dec 2021, Austin, TX, US.

On the numerical solution of a free end-time homicidal chauffeur game

Calà Campana, De Marchi, Borzì, Gerdts. (2020)

[ abstract | pdf | bibtex ]

@article{calacampana2021numerical,
    author      = {Cal{\`a}~Campana, Francesca and De~Marchi, Alberto and Borz{\'i}, Alfio and Gerdts, Matthias},
    title       = {On the numerical solution of a free end-time homicidal chauffeur game},
    journal     = {ESAIM: ProcS},
    year        = {2021},
    volume      = {71},
    pages       = {33--42},
    doi         = {10.1051/proc/202171104},
}

ESAIM: Proceedings and Surveys 71, pp. 33–42 (2021).
FGS'2019 — 19th French-German-Swiss conference on Optimization, Sep 2019, Nice, FR.

Constrained and sparse switching times optimization via augmented Lagrangian proximal methods

De Marchi. (2019)

[ abstract | pdf | bibtex ]

@inproceedings{demarchi2020constrained,
    author      = {De~Marchi, Alberto},
    title       = {Constrained and sparse switching times optimization via augmented {L}agrangian proximal methods},
    year        = {2020},
    month       = {7},
    pages       = {3633--3638},
    booktitle   = {2020 {A}merican {C}ontrol {C}onference ({ACC})},
    address     = {Denver, CO, USA},
    publisher   = {IEEE},
    issn        = {2378-5861},
    doi         = {10.23919/ACC45564.2020.9147892},
}

2020 American Control Conference (ACC), pp. 3633–3638, Jul 2020, Denver, US.

Sparse switching times optimization and a sweeping Hessian proximal method

De Marchi, Gerdts. (2019)

[ abstract | pdf | bibtex ]

@inproceedings{demarchi2020sparse,
    author      = {De~Marchi, Alberto and Gerdts, Matthias},
    title       = {Sparse switching times optimization and a sweeping {H}essian proximal method},
    year        = {2020},
    pages       = {89--95},
    booktitle   = {Operations Research Proceedings 2019},
    editor      = {Neufeld, Janis S. and Buscher, Udo and Lasch, Rainer and M{\"o}st, Dominik and Sch{\"o}nberger, J{\"o}rn},
    address     = {Cham},
    publisher   = {Springer International Publishing},
    isbn        = {978-3-030-48439-2},
    doi         = {10.1007/978-3-030-48439-2_11},
}

Operations Research (OR), pp. 89–95, Sep 2019, Dresden, DE.

Nonsmooth Newton's method: Some structure exploitation

De Marchi, Gerdts. (2019)

[ abstract | pdf | bibtex | code ]

@incollection{demarchi2019nonsmooth,
    author      = {De~Marchi, Alberto and Gerdts, Matthias},
    title       = {Nonsmooth {N}ewton's method: Some structure exploitation},
    year        = {2019},
    pages       = {409--420},
    booktitle   = {ICCS 2019, LNCS 11538},
    editor      = {J. M. F. Rodrigues et al.},
    publisher   = {Springer},
    doi         = {10.1007/978-3-030-22744-9_32},
}

International Conference on Computational Science (ICCS), pp. 409–420, Jun 2019, Faro, PT.
Lecture Notes in Computer Science, vol. 11538.

An iterative method for final time optimization in nonlinear optimal control

De Marchi, Gerdts. (2019)

[ abstract | pdf | bibtex ]

@incollection{demarchi2019iterative,
    author      = {De~Marchi, Alberto and Gerdts, Matthias},
    title       = {An iterative method for final time optimization in nonlinear optimal control},
    year        = {2019},
    pages       = {60--66},
    booktitle   = {2019 Proceedings of the Conference on Control and its Applications},
    publisher   = {SIAM},
    doi         = {10.1137/1.9781611975758.10},
}

SIAM Conference on Control and its Applications (CT), pp. 60–66, Jun 2019, Chengdu, CN.

An iterative solution approach for a bi-level optimization problem for congestion avoidance on road networks

Britzelmeier, De Marchi, Gerdts. (2017)

[ abstract | pdf | bibtex ]

@incollection{britzelmeier2018iterative,
    author      = {Britzelmeier, Andreas and De~Marchi, Alberto and Gerdts, Matthias},
    title       = {An iterative solution approach for a bi-level optimization problem for congestion avoidance on road networks},
    year        = {2018},
    pages       = {23--38},
    booktitle   = {Numerical Methods for Optimal Control Problems},
    editor      = {Falcone, Maurizio and Ferretti, Roberto and Gr{\"u}ne, Lars and McEneaney, William M.},
    publisher   = {Springer International Publishing},
    doi         = {10.1007/978-3-030-01959-4_2},
}

Numerical Methods for Optimal Control Problems, Springer INdAM Series 29, 23–38 (2018).

Traffic flow on single-lane road networks: Multiscale modelling and simulation

De Marchi, Gerdts. (2017)

[ abstract | pdf | bibtex ]

@article{demarchi2018traffic,
    author      = {De~Marchi, Alberto and Gerdts, Matthias},
    title       = {Traffic flow on single-lane road networks: Multiscale modelling and simulation},
    journal     = {IFAC-PapersOnLine},
    year        = {2018},
    pages       = {162--167},
    volume      = {51},
    number      = {2},
    doi         = {10.1016/j.ifacol.2018.03.028},
}

IFAC-PapersOnLine 51(2), 162–167 (2018).
9th Vienna International Conference on Mathematical Modelling (MATHMOD), Mar 2018, Vienna, AT.

Optimal control of a laser source to generate a minimum time trajectory of a droplet in a liquid layer

Biral, Bertolazzi, Bosetti, De Marchi, Hanczyc. (2016)

[ abstract | pdf | bibtex ]

This paper describes the use of optimal control theory applied to the motion of a low-power laser beam to precisely move a droplet in a liquid layer by means of the force on the liquid-liquid interface arising due to the surrounding thermal field (thermocapillary force and Marangoni effect). The form of heat field equations is approximated by the solution of a finite sum of laser pulses, whose analytical solution can be explicitly derived. In this way, the model of the system does not contain any partial differential equation (PDE). Optimization is performed by using the direct approach method and the fmincon solver provided by MATLAB. The initial guess is found with a simple model predictive controller. Perspective applications of this technology include beam-controlled targeting of pharmaceuticals in organic tissues.

@inproceedings{biral2016optimal,
    author      = {Biral, Francesco and Bertolazzi, Enrico and Bosetti, Paolo and De~Marchi, Alberto and Hanczyc, Martin M.},
    title       = {Optimal control of a laser source to generate a minimum time trajectory of a droplet in a liquid layer},
    booktitle   = {2016 Future Technologies Conference (FTC)},
    year        = {2016},
    pages       = {1208--1216},
    doi         = {10.1109/FTC.2016.7821754},
}

2016 Future Technologies Conference (FTC), pp. 1208–1216, Dec 2016, San Francisco, US.

Theses

Augmented Lagrangian and Proximal Methods for Constrained Structured Optimization

De Marchi. (2021)

[ abstract | pdf | bibtex ]

This thesis aims at investigating and developing numerical methods for finite dimensional constrained structured optimization problems. These provide a modeling framework for a variety of applications, as they offer a simple yet expressive language to formulate a broad class of problems. An algorithm is proposed that interlaces proximal methods and the augmented Lagrangian scheme. Relying on theoretical results, convergence guarantees are established for nonconvex problems. The inner subproblems can be solved by any method for structured optimization and the overall algorithm can be made matrix-free. Illustrative examples show the benefits of constrained structured programs as a modeling tool and of a careful problem formulation. When tested and compared on small to medium-size nonlinear programming benchmark problems, the proposed method prove competitive against a state-of-the-art solver. The proposed framework is adopted in the context of switching time optimization for constrained mixed-integer optimal control with switching costs. We describe the reformulation as constrained structured programs via the cardinality function, and discuss possible extensions to deal with more general problems. Then, we prove that this formulation satisfies the assumptions underlying the proximal augmented Lagrangian algorithm. Numerical examples show the filtering action of switching costs, which rules out chattering solutions. Finally, we develop a primal-dual Newton-type proximal method for convex quadratic programming. This is based on the proposed proximal augmented Lagrangian framework and weaves together the proximal point algorithm and a damped semismooth Newton's method. The outer proximal regularization yields a numerically stable method, and we interpret the proximal operator as the unconstrained minimization of the primal-dual proximal augmented Lagrangian function. The inner tailored Newton's scheme is fast, the linear systems are always solvable, and exact linesearch can be performed. The method handles degenerate problems, provides a mechanism for infeasibility detection, and exploits warm starting, while requiring only convexity. Numerical results against full-fledged solvers demonstrate our method is robust and efficient. All proposed algorithms are implemented in software packages that allow for the generic, efficient solution of problems using the methods developed in this thesis.

@phdthesis{demarchi2021dissertation,
    author      = {De~Marchi, Alberto},
    title       = {Augmented {L}agrangian and Proximal Methods for Constrained Structured Optimization},
    year        = {2021},
    month       = {6},
    school      = {University of the Bundeswehr Munich},
	address     = {Munich, Germany},
    doi         = {10.5281/zenodo.4972535},
}

University of the Bundeswehr Munich, Jun 2021.
🏆 Forschungspreis ITIS e. V.

Modelling and Optimal Control of Laser-Driven Thermocapillary Motion of a Droplet

De Marchi. (2016)

[ abstract | pdf | bibtex ]

@mastersthesis{demarchi2016mscthesis,
    author      = {De~Marchi, Alberto},
    title       = {Modelling and optimal control of laser-driven thermocapillary motion of a droplet},
    year        = {2016},
    month       = {10},
    school      = {University of Trento},
    doi         = {10.5281/zenodo.1481663},
}

University of Trento, Oct 2016.