@techreport {herrmann2014pmpde,
	title = {A penalty method for PDE-constrained optimization},
	number = {WO 2014/172787},
	year = {2014},
	note = {(International publication date 30 October 2014. International publication number WO 2014/172787.)},
	month = {10},
	institution = {UBC},
	type = {Patent},
	abstract = {The invention is directed to a computer-implemented method for obtaining a physical model having physical model parameters wherein solutions to one or more partial-differential-equations (PDE{\textquoteright}s) are calculated ans wherein (i) an appropriate initial model is selected, (ii) setup a system of equations referred to as the data-augmented PDE for the field, comprising of the discretized PDE, the sampling operator, the source function and the observed data, and solve the data-augmented PDE in a suitable manner to obtain a field that both satisfies the PDE and fits the data to some degree, (iii) setup a system of equations by using the PDE, the source function and the field obtained in step (ii) and solve this system of equations in a suitable manner to obtain an update of the physical model parameters and repeat steps (ii)-(iii) until a predetermined stopping criterion is met.},
	keywords = {Optimization, patent, penalty method},
	url = {https://slim.gatech.edu/Publications/Public/Patents/2014/herrmann2014pmpde/herrmann2014pmpde_WO2014172787.pdf},
	url2 = {http://patentscope.wipo.int/search/en/WO2014172787},
	author = {Felix J. Herrmann and Tristan van Leeuwen}
}
@techreport {vanLeeuwen2013Penalty2,
	title = {A penalty method for PDE-constrained optimization},
	number = {TR-EOAS-2013-6},
	year = {2013},
	month = {04},
	institution = {UBC},
	abstract = {We present a method for solving PDE constrained optimization problems based on a penalty formulation. This method aims to combine advantages of both full-space and reduced methods by exploiting a large search-space (consisting of both control and state variables) while allowing for an efficient implementation that avoids storing and updating the state-variables. This leads to a method that has roughly the same per-iteration complexity as conventional reduced approaches while dening an objective that is less non-linear in the control variable by implicitly relaxing the constraint. We apply the method to a seismic inverse problem where it leads to a particularly ecient implementation when compared to a conventional reduced approach as it avoids the use of adjoint state-variables. Numerical examples illustrate the approach and suggest that the proposed formulation can indeed mitigate some of the well-known problems with local minima in the seismic inverse problem.},
	keywords = {Optimization, waveform inversion},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2013/vanLeeuwen2013Penalty2/vanLeeuwen2013Penalty2.pdf},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
@techreport {vanleeuwen2012smii,
	title = {A parallel matrix-free framework for frequency-domain seismic modelling, imaging and inversion in Matlab},
	number = {TR-EOAS-2012-5},
	year = {2012},
	month = {07},
	abstract = {I present a parallel matrix-free framework for frequency-domain seismic modeling, imaging and inversion. The framework provides basic building blocks for designing and testing optimization-based formulations of both linear and non-linear seismic in- verse problems. By overloading standard linear-algebra operations, such as matrix-vector multiplications, standard optimization packages can be used to work with the code without any modification. This leads to a scalable testbed on which new methods can be rapidly prototyped and tested on medium-sized 2D problems. I present some numerical examples on both linear and non-linear seismic inverse problems.},
	keywords = {Matlab, object-oriented programming, Optimization, seismic imaging},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2012/vanleeuwen2012smii/vanleeuwen2012smii.pdf},
	author = {Tristan van Leeuwen}
}
@techreport {vanleeuwen2012SEGparallel,
	title = {A parallel, object-oriented framework for frequency-domain wavefield imaging and inversion.},
	number = {TR-EOAS-2012-2},
	year = {2012},
	month = {04},
	institution = {Department of Earth and Ocean Sciences},
	address = {University of British Columbia, Vancouver},
	abstract = {We present a parallel object-oriented matrix-free framework for frequency-domain seismic modeling, imaging and inversion. The key aspects of the framework are its modularity and level of abstraction, which allows us to write code that reflects the underlying mathematical structure and develop unit-tests that guarantee the fidelity of the code. By overloading standard linear-algebra operations, such as matrix-vector multiplications, we can use standard optimization packages to work with our code without any modification. This leads to a scalable testbed on which new methods can be rapidly prototyped and tested on medium-sized 2D problems. Although our current implementation uses (parallel) Matlab, all of these design principles can also be met by using lower-level languages which is important when we want to scale to realistic 3D problems. We present some numerical examples on synthetic data.},
	keywords = {Imaging, inversion, Modeling, SEG},
	url = {https://slim.gatech.edu/Publications/Public/TechReport/2012/vanleeuwen2012SEGparallel/vanleeuwen2012SEGparallel.pdf},
	author = {Tristan van Leeuwen and Felix J. Herrmann}
}
