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Let φ and ψ be regular quadratic forms over a field F of characteristic different from 2. We say that ψ is a quasisubform of φ if there is a∈F* such that aψ is a subform of φ. Let L/F be an odd deg...

In this paper, a family of coordinate majorization descent algorithms are proposed for solving the nonconvex penalized learning problems including SCAD and MCP estimation. In the coordinate majoriz...

Given a convex objective function on a Banach space, which is Lipschitz on bounded sets, we consider the class of regular vector fields introduced in our previous work on descent methods. We analyz...

To solve a large-scale unconstrained optimization problem, in this paper we propose a class of spectral three-term conjugate gradient methods. We indicate that the proposed class, in fact, generate...

This paper begins with a brief review of affine invariance and its significance for iterative algorithms. It then explores the existence of affine invariant descent directions for unconstrained min...

The British writer J G Ballard is known for his distinctive treatments of the familiar and the everyday in organized society as vulnerable to rupture and descent into violence and chaos. Never straightforwardly dystopian, Ballard was capable of insightful analysis that revealed the strangeness of particular qualities of lived experience, challenging his audience to question their place in the order of things. Raised in Shanghai, Ballard’s wartime experiences exposed him to the extremes of human behaviour and to the stripping away of the veneers of conventional civilized norms. More than mere biographical markers, this article argues that through a range of works, Ballard offers us a phenomenological account of the worst of the conditions under which he lived, particularly at the close of the Japanese war in Shanghai, one that captures the lived experience of the absence of law.

At the end of Scene 3, in what is arguably a parody of the famous balcony scene in Romeo and Juliet, Stanley Kowalski emerges drunk, half naked and emotional after his game of poker has erupted int...

Given a Lipschitz convex and coercive objective function on a Banach space, we revisit the class of regular vector fields introduced in our previous work on descent methods. Taking into account com...

Stephen M. Lyon’s Political Kinship in Pakistan examines the contestations of political power at both local and central levels through the prism of kinship that permeates the foundations of Pakista...

The Italian Enlightenment is one of the great intellectual achievements of Europe’s siecle des lumieres. Its two branches, the Lombard branch together with the Neapolitan, both cooperate to produci...

Since 1947, the Canadian Citizenship Act has set out the laws that determine eligibility for Canadian citizenship. Throughout the Act’s various enactments, the Canadian government has recog...

In this paper, based on the numerical efficiency of Hestenes–Stiefel (HS) method, a new modified HS algorithm is proposed for unconstrained optimization. The new direction independent of the line search satisfies in the sufficient descent condition. Motivated by theoretical and numerical features of three-term conjugate gradient (CG) methods proposed by Narushima et al., similar to Dai and Kou approach, the new direction is computed by minimizing the distance between the CG direction and the direction of the three-term CG methods proposed by Narushima et al. Under some mild conditions, we establish global convergence of the new method for general functions when the standard Wolfe line search is used. Numerical experiments on some test problems from the CUTEst collection are given to show the efficiency of the proposed method.

In this paper, we study properties of a special class of ordered median functions, called block-functions. These are ordered median functions which belong to a generating binary (row)-vector of the form called a block vector. The aim of this paper is to explicitly determine the simplicial complexes and all steepest descent and ascent directions of descent and ascent cones of ordered median block-function.

In this paper, we propose a non-monotone line search method for solving optimization problems on Stiefel manifold. The main novelty of our approach is that our method uses a search direction based on a linear combination of descent directions and a Barzilai–Borwein line search. The feasibility is guaranteed by projecting each iterate on the Stiefel manifold through SVD (singular value decomposition) factorizations. Some theoretical results for analysing the algorithm are presented. Finally, we provide numerical experiments for comparing our algorithm with other state-of-the-art procedures. The code is available online. The experimental results show that the proposed algorithm is competitive with other approaches and for particular problems, the computational performance is better than the state-of-the-art algorithms.

The article presents a theoretical argument for aligning principles of citizenship with realities of migrant transnationalism and dual citizenship. Migrant transnationalism and dual citizenship challenge zero-sum understandings of belonging and residence as rooted in one place only. Through the lens of residence, the authors connect insights from migrant transnationalism literature with citizenship studies’ focus on principles of citizenship. Principles of citizenship based on descent and birthplace build on particular genealogies of belonging that define membership, and are the basis on which citizenship is granted. Neither of the two principles provides adequate answers to how naturalisation, in terms of belonging to the political community, can be justified as anything other than exceptions. Jus domicili offers a complementary alternative, wherein belonging is connected to residence, thus moving naturalisation out of the realm of exceptions. A configuration of principles of citizenship that is ...

As the title indicates, this ambitious book aims to provide a global survey of rulers and dynasties during a time when elite families governing by descent were the most common form of government. L...

Darryl Leroux’s recent work delineates the insidious twists and turns of the claims to Indigeneity made by contemporary white French-settler descendants (Quebecois). Through a thorough excavation a...

We prove that for any finite dimensional representation V of a finite group G of order n the quotient variety G∖ℙ(V) is projectively normal with respect to descent of 𝒪(1)⊗l where l = lcm{1,2,3,4,…,n}. We also prove that for the tautological representation V of the alternating group An the projective variety An∖ℙ(V) is projectively normal with respect to the descent of the above line bundle.

This paper asks what mestizaje as presently conceived could have meant in colonial Latin America before modern notions of race, nation, state, or culture. It explores the term ladino in contemporary Chiapas and Guatemala that refers to people of mixed descent who identify as ‘not Indian.’ More than a substitute for mestizo, ladino represents a descent ideology that stresses parentage over race in pursuit of relative advantage within a stratified, postconquest society. This descent ideology in turn derives from the ‘republics’ of Spaniards and Indians – and African slaves – in colonial Guatemala, and post-Reconquest Iberian ideals of ‘purity of blood’ based on, not race, but legitimate birth to a Christian family going back to before the Muslim conquest of Spain. The vagaries of genealogical reckoning inherent in descent ideologies help to rationalize why from the bottom up ‘mestizo’ identities came to depend as much on behavior as appearance, and from the top down, they provoked blanket phenotypic...

In this paper, we show how a nonlinear scalarization functional can be used in order to characterize several well-known set order relations and which thus plays a key role in set optimization. By means of this functional, we derive characterizations for minimal elements of set-valued optimization problems using a set approach. Our methods do not rely on any convexity assumptions on the considered sets. Furthermore, we develop a derivative-free descent method for set optimization problems without convexity assumptions to verify the usefulness of our results.

A few years ago, the authors proposed a nature-inspired metaheuristic concept, the spiral optimization algorithm, which was inspired by spiral phenomena in nature. The principal idea of the algorit...

The archetypal descent into hell can provide a paradigm for the representation of trauma, which is often theorized as being unrepresentable. Mark Z. Danielewski's House of Leaves (2000) models the experience of psychological trauma on the archetypal descent into hell, or katabasis. House of Leaves thus challenges a certain strand of poststructuralism that has become dominant within literary critical circles of trauma studies. Ultimately, Danielewski manipulates the paradigm of katabasis to forge what I style an infernal phenomenal reference system to represent the hell of trauma.

We suggest a modification of the descent splitting methods for decomposable composite optimization problems, which maintains the basic convergence properties, but enables one to reduce the computational expenses per iteration and to provide computations in a distributed manner. It consists of making coordinate-wise steps together with a special threshold control.

This article concerns optimal control and stabilization for some Fisher-like models with control acting in a subdomain ω. We investigate the optimal position of ω for some optimal harvesting problems. First, we refer to a logistic model with diffusion. We remember the necessary optimality conditions, and then obtain an iterative method to improve the position of ω for the optimal harvesting effort (for a simplified model without logistic term). Next, we consider the null stabilization for a controlled Fisher model and obtain a descent method to improve the position of ω in order to get a faster stabilization to zero. Numerical tests illustrating the effect of the last method are given. We also studied the null stabilization for a prey-predator system and have reduced it to the study of the null stabilizability for a related Fisher model.

The current ruling house in Tonga, that of the Tuʻi Kanokupolu, includes 13 chiefly lines directly descended from that family. Plausible, full accounts of the antecedents of all these hereditary title-holders exist, with one exception. Both formal and informal descriptions of the descent of the Lasike title include anomalous gaps that demand explanation. This paper uses previously unnoticed sources in an attempt to fill in the gaps, offering powerful reasons why the known bearers of the title might not have wanted to remember their entire line of descent.

Bregman iterative algorithms have been extensively used for and total variation regularization problems, allowing to obtain simple, fast and effective algorithms. In this paper, three already-available algorithms for geosounding inversion are modified by including them in a Bregman iterative procedure. The resulting algorithms are easy to implement and do not require any optimization package. Modelling results are presented for synthetic and field data, observing better convergence properties than the original versions, avoiding the need of any continuation descent procedure.

International audience; We consider a simplied model of a coupled parabolic PDE-ODE describing heat transfer within buildings. We describe an identication procedure able to reconstruct the parameters of the model. The response of the model is nonlinear with respect to its parameters and the reconstruction of the parameters is achieved by the introduction of a new vectorial descent stepsize, which improves the convergence of the Levenberg-Marquardt minimization algorithm. The new vectorial descent stepsize can have negative and positive entries of different sizes, which fundamentally differs from standard scalar descent stepsize. The new algorithm is proved to converge and to outperform the standard scalar descent strategy. We also propose algorithms for the initialization of the parameters needed by the reconstruction procedure, when no a priori knowledge is available.

An ordered median functions is a continuous piecewise-linear function. It is well known that in finite dimensional spaces every continuous piecewise-linear function admits a max-min representation in terms of its linear functions. An explicit representation of an ordered median function in max-min form is given by the authors and will appear in a forthcoming issue of this journal. Based on this representation, we give a topological classification of ordered median functions through their simplicial complex of ascent (resp. descent) cones.

We consider the monotone composite variational inequality CVI where the underlying mapping is formed as the sum of two monotone mappings. We combine the forward–backward and descent direction ideas together, and thus present the unified algorithmic framework of forward–backward-based descent methods for solving the CVI. A new iterate of such a method is generated by a prediction–correction fashion, where the predictor is yielded by the forward–backward method and then the predictor is corrected by a descent step. We derive some implementable forward–backward-based descent algorithms for some concrete cases of the CVI, and verify their numerical efficiency via preliminary numerical experiments.

In [Zhou, A short note on the global convergence of the unmodified PRP method, Optim. Lett. doi: 10.1007/s11590-012-0511-7, to appear], Zhou showed that the classical unmodified Polak–Ribiere–Polyak PRP nonlinear conjugate gradient method converges globally in the sense that lim infk→∞‖∇fxk‖=0 for nonconvex minimization by the use of some nonmonotone line search. In this paper, we present a new non-descent backtracking type line search and show that the PRP method has strongly global convergence property i.e. lim k→∞‖∇ fxk‖=0 and locally R-linear convergence rate for nonconvex optimization with the proposed line search by suitably choosing the initial stepsize. Some numerical results compared with existing descent type line searches are reported.

Within the phrase ‘cultural conflict’ in its title, this book hints at a throwback to a time when the history of leisure was bound up with notions of social control. But rather than a descent into ...

In this paper, a modified Polak–Ribi‘ere–Polyak MPRP conjugate gradient method for smooth unconstrained optimization is proposed. This method produces at each iteration a descent direction, and this property is independent of the line search adopted. Under standard assumptions, we prove that the MPRP method using strong Wolfe conditions is globally convergent. The results of computational experiments are reported and show the effectiveness of the proposed method.

The equilibrium problem (EP) can be formulated as an unconstrained minimization problem through the D-gap function. We present a descent type algorithm for solving EP based on the generalized D-gap function. We discuss the convergence properties of the proposed algorithm under suitable assumptions while supporting our approach with appropriate examples. We construct an error bound for the equilibrium problem interms of the generalized D-gap function which gives a significant modification to the error bound given by Konnov et al.

New algorithms for solving unconstrained optimization problems are presented based on the idea of combining two types of descent directions: the direction of anti-gradient and either the Newton or quasi-Newton directions. The use of latter directions allows one to improve the convergence rate. Global and superlinear convergence properties of these algorithms are established. Numerical experiments using some unconstrained test problems are reported. Also, the proposed algorithms are compared with some existing similar methods using results of experiments. This comparison demonstrates the efficiency of the proposed combined methods.

This paper examines the ways in which 12 high school students of Mexican descent remain resilient amid difficult and stressful realities. Through an examination of students' interview responses, a case is made that students' ability to engage in school and figure out everyday ways to partake as students are signs of resilience. This work suggests the need to shift from a focus on single, specific stressful situations or experiences to a more accurate and less essentialized understanding of both constraints and capabilities around student engagement and well-being.

In this article we will give relation between ascent and descent of a Banach space operator T and its diagonal (i.e. its restriction A to an invariant subspace and the induced quotient mapping B). This result is then applied to describe Drazin invertibility of one of these three operators using Drazin invertibility of the other two operators. It is proved that the operator T is meromorphic if and only if A and B are meromorphic.

We characterize the ascent and descent directions for the modulus of a complex polynomial p(z) at an arbitrary point z0 in the complex plane. We prove that when p(z0) ≠ 0, the cones of ascent and d...

This article explores how young people (aged 8–18) of Latin American descent living in the north of England negotiate sameness and belonging within a context of socio-cultural invisibility (sparse presence of Latin Americans). It is argued that these young people, who are characterised by a diversity of marked and unmarked embodiments, use in/visibility strategies in order to navigate the visual regime of ethno-cultural difference which characterises their integration context. With these strategies, they either reproduce notions of sameness or enact forms of cultural diversity to gain membership to the places where they live.

In this article we propose two algorithms for minimization of quasiconvex functions. The first one is of type subgradient. In the second one, we consider the steepest descent method with Armijo's rule. In both, we use elements from Plastria's lower subdifferential. Under certain conditions, we prove that the sequence generated by these algorithms globally converges to a solution. We provide a counter-example showing that the choice of the minus gradient direction does not assure the global convergence of the descent method to a solution. This counter-example is related to a mistake in the proof of the Theorem 3.1 of J.P. Dussault, [Convergence of implementable descent algorithms for unconstrained optimization (technical note), J. Optim. Theory Appl. 104 (2000), pp. 739–745]. We also point out the mistake in the proof of that theorem.

It was earlier demonstrated, by the so-called main (or simplest) problem of the Calculus of Variations, that the Theory of Exact Penalties allows one not only to derive fundamental results of the Calculus of Variations but also to construct new direct numerical methods for solving variational problems based on the notions of subgradient and hypogradient of the exact penalty function (which is essentially nonsmooth even if all initial data are smooth). In this article Exact Penalties are used to solve isoperimetric problems of the Calculus of Variations. New direct numerical methods are described (e.g. the method of hypodifferential descent). Several numerical examples are discussed.

In this article, a new method is proposed for solving symmetric nonlinear equations, which can ensure that the search direction is descent for the norm function without carrying any line search technique. Under mild conditions, the global convergence of the given method is established. Numerical results show that the proposed method is effective for the given test problems.

We present an algorithm to locally minimize nonsmooth, nonconvex functions. In order to find descent directions, the notion of quasisecants, introduced in this paper, is applied. We prove that the algorithm converges to Clarke stationary points. Numerical results are presented demonstrating the applicability of the proposed algorithm to a wide variety of nonsmooth, nonconvex optimization problems. We also compare the proposed algorithm with the bundle method using numerical results.

A globally convergent algorithm for equilibrium problems with differentiable bifunctions is proposed. The algorithm is based on descent directions of a suitable family of gap functions. The novelty of the approach is that assumptions which guarantee that the stationary points of the gap functions are global optima are not required.

From Africa to the Caribbean to Panama and to the United States and back, the history and culture of Panamanians of Afro-Antillean descent is layered with struggle and survival. These photographs document a culture that may not exist in the future, stitching together a representation of a generation for whom locality was everything, and a generation that have come from a time that while they did not feel a need to identify themselves, they also felt no need to question the continuity of their culture.

An iterative strategy for the reconstruction of objects buried in a medium and the identification of their material parameters is analysed. The algorithm alternates guesses of the domains using topological derivatives with corrections of the parameters obtained by descent techniques. Numerical experiments in geometries with multiple scatterers show that our scheme predicts the number, location and shape of objects, together with their physical parameters, with reasonable accuracy in a few steps.