The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning

In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced (not necessarily minimal) objective function values. The superiorization methodology is based on interlacing the iterative steps of two separate and independent iterative processes by perturbing the iterates of one process according to the steps dictated by the other process. We include in our developed method two novel elements. The first one is the permission to restart the perturbations in the superiorized algorithm which results in a significant acceleration and increases the computational efficiency. The second element is the ability to independently superiorize subvectors. This caters to the needs of real-world applications, as demonstrated here for a problem in intensity-modulated radiation therapy treatment planning.The work of Yair Censor was supported by the ISF-NSFC joint research plan Grant Number 2874/19. Francisco Aragón and David Torregrosa were partially supported by the Ministry of Science, Innovation and Universities of Spain and the European Regional Development Fund (ERDF) of the European Commission, Grant PGC2018-097960-B-C22, and the Generalitat Valenciana (AICO/2021/165). David Torregrosa was supported by MINECO and European Social Fund (PRE2019-090751) under the program “Ayudas para contratos predoctorales para la formación de doctores” 2019

The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning

In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced (not necessarily minimal) objective function values. The superiorization methodology is based on interlacing the iterative steps of two separate and independent iterative processes by perturbing the iterates of one process according to the steps dictated by the other process. We include in our developed method two novel elements. The first one is the permission to restart the perturbations in the superiorized algorithm which results in a significant acceleration and increases the computational efficiency. The second element is the ability to independently superiorize subvectors. This caters to the needs of real-world applications, as demonstrated here for a problem in intensity-modulated radiation therapy treatment planning.Comment: Revised version, October 10, 2022; accepted for publication in: Applied Mathematics and Computatio

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Ethics of climate change: a normative account

Consider, for instance, you and your family have lived around a place where you enjoyed the flora and fauna of the land as well as the natural environment. Fishing and farming were pleasant activities for your family, and anyone in the community not only to survive but thrive. Your neighbours and the people in the community pride themselves so much in their farming abilities and fishing techniques. Suddenly things start taking a different turn because of rising sea level and changing weather pattern. First, your land began to give way because of sweeping erosion, and later the riverbank serving the community starts drying up. Your neighbour could not hold their own in this grim condition as they started relocating. You even witnessed some of your family and friends leaving the community and you later heard that they have become climate refugees. To put it all together, you were told that what you are experiencing is one of climate change effects. You were told that the loss of the place that you once cherished is not an act of God but the result of the reckless flaring of greenhouse gasses harmful to the environment by some powerful but polluting nations. What will you do? This might sound like a fairy tale. In reality, this is the story of the people of Saint Louis Atlantic Coasts in Senegal, captured by the Global Climate Change Alliance Plus Initiative.1 Their situation has been described as ‘living on the edge’ because for centuries, Saint Louis Atlantic Coasts, home to around 230,000 inhabitants, also known as the ‘Venice of Africa’ has been protected from the pounding Atlantic waves by the ‘Langue de Barbarie,’ a narrow, 30 km peninsula at the mouth of the Senegal river. However, the low-lying sandy spit of land along this World Heritage site is itself rapidly disappearing in the present. This is the consequence of a changing climate and other man-made problems such as illegal sand-mining and over-development. Today, the southern part of the Langue de Barbarie is an island, and the village of Doune Baba Dieye is under more than a metre of water. The villagers have become climate refugees, forced to live in temporary camps on the mainland. Not only have they lost their homes, but they have also lost significant cultural heritage like the farming and fishing culture tied to this place. The ethical considerations that emerge from climate change impacts on the world’s cultural heritage are varied. However, it seems not as self-evident in the way that research on climate change ethics has been framed around economic interest and direct threats to human life and other species. Even when they mention climate impacts on heritage sites around the world, those of Africans have been side-lined. For instance, the impact of climate change on small island nations like Tuvalu, Kiribati2 have gained much traction in climate change discourse, but we do not get to see stories of Africans whose cherished cultural heritage are affected by climate despoliation. How do we respond to this intractable challenge? This is a question of justice and, to be more precise, climate justice. Many principles and proposals for climate justice have been put forward, but the insufficient attention to the vulnerabilities or loss of cultural heritage values of Africans, which is a critical aspect of their social realities, make these theories less persuasive on a global level. This thesis, then, fills this gap in the literature by suggesting that the failure to take cognizance of the injustice in neglecting cultural heritage values when dealing with the burden of climate change is the effect of three problems. One, the value of culture is less understood in this environmental age. Hence, cultural values are excluded or made to be secondary in consideration of principles of climate justice. Second, the idea of Personhood has been neglected in climate ethics and climate justice discourse. Yet, this idea of Personhood can be an enabler of climate justice in that a realization of the significance of cultural heritage to the wellness of the human persons in Africa, makes it loss morally reprehensible. Third, those whose cultural heritage is significantly affected do not get represented in the debate about sharing the burden of climate change. This dissertation thereby builds upon the general findings of the past about anthropogenic climate change, its causes and consequences. Adopting a discursive normative framework, I also address the significance of cultural heritage in this contemporary environmental age and discuss the global justice implications of cultural heritage loss to climate change. This dissertation further provides a critique of mainstream climate justice theories, especially their marginalization of the cultural dimension of climate change. In this regard, the metaphor - ‘cultural storm’ was deployed to argue that climate justice discourses have neither factored the deep socio-cultural impact of climate change nor do they draw on the cultural understanding of justice in putting forward their theories. Given the nature of the indirect, cumulative, and interconnected invisible losses to cultural heritage from climate change, it seems unlikely that they can be addressed by simple tweaks of the climate justice status quo. This dissertation proposes that the idea of personhood in African philosophy, can be conceived to ensure climate justice live up to its expectations in a world of diverse persons dealing with a complex phenomenon like climate change. It argues that a cultural dimension of climate ethics has implications for how mitigation, adaptation and compensation plans should be furthered for global climate justice. At the foundation of my argument, I suggest that what is needed in climate justice discourse is a commitment to explore new and innovative alternatives that will produce an inclusive global climate treaty that is sensitive to the cultural heritage assets that is destroyed by climate change in Africa. This will require a multi-dimensional framework that allows fundamentally different kinds of values and benefits to be given equal visibility and standing in global climate negotiations. The dissertation proceeds in six chapters. In the first chapter, I discuss how climate change denies, damage and destroys cultural heritage values in Africa and argue that it is unjust to ignore this dimension of climate change impact, particularly on the African continent. In the second chapter, I critically discuss the normative value of cultural heritage in an environmentally sustainable and morally appropriate way for this global age. I argue that what is lost when climate change affects cultural heritage is a significant cultural asset that ought to be seriously considered in climate ethics. The third chapter addresses the global justice implications of the destruction of Africa's cultural heritage by climate change that must be paid attention to. In chapter four, I evaluate the plausibility of some of the mainstream climate justice proposals. I offered a different possible critique of current approaches to climate justice to show how they have furthered cultural injustice. The critique of current climate justice theories that I offer, stems from an uninspiring approach that belies logic permitting the sacrificing of that which is connected to others wellbeing as well as the implicit assumptions and the limitation of the idea of justice that undergird these climate justice theories. I offer, in chapter five, a plausible climate ethics theory that recognizes culturally embedded ideas of justice and empower all stakeholders to build by themselves, lives that are, in the light of these ideas, deemed to be adversely impacted by climate change. This theory advances a socio-cultural perspective to climate change which could provide a nuanced basis for understanding and addressing global climate duties that will be sensitive to the loss of cultural heritage. Specifically, I apply the African conception of personhood, to provide a normative basis for a different but intuitive understanding of the cultural dimension of climate ethics. In the final chapter, I discuss how this theory can be applied to rethink current global responses in the form of mitigation, adaptation and compensation in such a way that it takes seriously the impacts of climate change on Africa’s cultural heritage and values.Thesis (PhD) -- Faculty of Humanities, Philosophy, 202