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This study looks closely into the analysis of the variation of constants formula given by Φ (t) = S (t) Φ (0) + ∫ 0 t S (t − σ) F (σ , Φ (σ)) d σ , for t ∈ [ 0 , T ] , T > 0 , within the context of modular function spaces L ρ . Additionally, this research explores practical applications of the variation of constants formula in variable exponent Lebesgue spaces L p (·) . Specifically, the study examines these spaces under certain conditions applied to the exponent function p (·) and the functions F as well as the semigroup S (t) , utilizing the symmetry properties of the algebraic semigroup. This investigation sheds light on the intricate interplay between parameters and functions within these mathematical frameworks, offering valuable insights into their behavior and properties in L p (·) . [ABSTRACT FROM AUTHOR]

This paper develops a method to integrate user knowledge into the optimization process by simultaneously modelling feasible design space and optimizing an objective function. In engineering, feasible design space is a constraint similar to those in optimization problems. However, not all constraints can be explicitly written as mathematical functions. This includes manufacturing concerns, ergonomic issues, complex geometric considerations, or exploring material options for a particular application. There needs to be a way to integrate designer knowledge into the design process and, preferably, use that to guide an optimization problem. In this research, these constraints are modeled using classification surrogate models and incorporated with Bayesian optimization. By suggesting design options to a user and allowing them to box off areas of feasible and infeasible designs, the method models both the feasible design space and an objective function probability of new design targets that are more optimal and have a high probability of being feasible. This proposed method is first proven with test optimization problems to show viability then is extended to include user feedback. This paper shows that by allowing users to box off areas of feasible and infeasible designs, it can effectively guide the optimization process to a feasible solution. [ABSTRACT FROM AUTHOR]

Serverless computing is a new fine-grained computing and deploying paradigm which combined terminal devices, edge nodes and cloud data center into a complete computing system. Stateless function is the critical factor to implement serverless computing. For optimizing the function execution, function placement is becoming the urgent problem to be solved in the serverless computing. To specify what is function placement in serverless computing, an adaptive function placement framework is presented. For prejudging the trend of function placement, positive or negative properties of event are classed. Based on the positive or negative impact on the function placement decision and function placement trend, mathematical model of function placement is presented for the first time. For specifying the adaptive function placement in serverless computing, An adaptive function placement model is formulated based on the Markov Decision Process (MDP). In the model, function states space, placement rate, placement probability, decision time, action set, cost and criterion are presented for the first time to specify the computation of the function's MDP.The presented algorithm decides function execution in terminal devices,local edge nodes or the function execution in the remote available cloud servers in a real time and adaptive way. The presented algorithm also permits dynamically allocating functions to minimize the Dec(t) while keeping performance satisfaction. Evaluation and experiment show the presented adaptive function placement algorithm can get the satisfied requirements of different indexes. [ABSTRACT FROM AUTHOR]

We study approximation of periodic functions by arbitrary linear combinations of n translates of a single function. We construct some linear methods of this approximation for univariate functions in the class induced by the convolution with a single function, and prove upper bounds of the Lp-approximation convergence rate by these methods, when n → ∞, for 1 ≤ p ≤ ∞. We also generalize these results to classes of multivariate functions defined as the convolution with the tensor product of a single function. In the case p = 2, for this class, we also prove a lower bound of the quantity characterizing best approximation of by arbitrary linear combinations of n translates of arbitrary function. [ABSTRACT FROM AUTHOR]

In the present paper, we establish a theorem on best approximation of a function g 2 Bλ q (Lr) of its Fourier series. Our main theorem generalizes some known results of this direction of work. Thus, the results of [10], [26] and [27] become the particular case of our main Theorem 3.1. [ABSTRACT FROM AUTHOR]

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We study the dynamics of topologically Anosov homeomorphisms of non-compact surfaces. In the case of surfaces of genus zero and finite type, we classify them. We prove that if f : S → S, is a Topologically Anosov homeomorphism where S is a non-compact surface of genus zero and finite type, then S = R² and f is conjugate to a homothety or reverse homothety (depending on wether f preserves or reverses orientation). A weaker version of this result was conjectured in [6]. [ABSTRACT FROM AUTHOR]

We introduce the notion of umIO(X)-structures determined by operators mInt, mCl, mInt and mCl on an ideal minimal space (X,mX, I). By using umIO(X)-structures, we introduce and investigate a function f: (X,mX, I) ?(Y,s) called umI-continuous. As special cases of umI-continuity, we obtain m-semi-I -continuity [11], m-pre-I -continuity [10], m-α-I -continuity [2], m-b-I-continuity [15], and m-β-I -continuity [9]. [ABSTRACT FROM AUTHOR]

Estimating parameters for distributed hydrological models is a challenging and long studied task. Parameter transfer functions, which define model parameters as functions of geophysical properties of a catchment, might improve the calibration procedure, increase process realism, and can enable prediction in ungauged areas. We present the function space optimization (FSO), a symbolic regression method for estimating parameter transfer functions for distributed hydrological models. FSO is based on the idea of transferring the search for mathematical expressions into a continuous vector space that can be used for optimization. This is accomplished by using a text generating neural network with a variational autoencoder architecture that can learn to compress the information of mathematical functions. To evaluate the performance of FSO, we conducted a case study using a parsimonious hydrological model and synthetic discharge data. The case study consisted of two FSO applications: single‐criteria FSO, where only discharge was used for optimization, and multicriteria FSO, where additional spatiotemporal observations of model states were used for transfer function estimation. The results show that FSO is able to estimate transfer functions correctly or approximate them sufficiently. We observed a reduced fit of the parameter density functions resulting from the inferred transfer functions for less sensitive model parameters. For those it was sufficient to estimate functions resulting in parameter distributions with approximately the same mean parameter values as the real transfer functions. The results of the multicriteria FSO showed that using multiple spatiotemporal observations for optimization increased the quality of estimation considerably. Plain Language Summary: Hydrological models are widely used tools for predicting river runoff or other components of the hydrological cycle that are important for the management of water resources. Typically, processes in those models use parameters to characterize the unique aspect of the studied area. Usually, these parameters are optimized to produce a well‐performing prediction model. This potentially leads to a loss of their physical meaning. Preserving the physical meaning of model parameters can be achieved by defining them with a relationship to properties of the modeled area (soil properties, topography, etc). These relationships are given as mathematical equations that compute parameters from a set of geophysical properties. We here present a method to automatically estimate such equations, called function space optimization (FSO). FSO transfers the search for mathematical equations into an optimization problem by using a neural network to encode the information of potential equations. We show FSO's ability in a case study using a hydrological model and synthetic runoff data. The results show that FSO is able to approximate the true relationship sufficiently. Furthermore, we show that additional spatial observation data can increase FSO performance. Key Points: This study introduces a method to infer transfer functions for the multiscale parameter regionalization approachWe demonstrate its ability in a case study using synthetic runoff dataWe show that multicriteria optimization can improve the estimation of parameter transfer functions [ABSTRACT FROM AUTHOR]

this paper, we discuss about bounded, isometric and hypercyclic composition operators on Cesáro function spaces. [ABSTRACT FROM AUTHOR]

The aim of this paper is to discuss the Besov spaces bounds for semiclassical Fourier integral operator. We give the conditions that the symbol and the phase function must satisfy for this operator to be bounded. [ABSTRACT FROM AUTHOR]

We study in this article the mathematical properties of a class of orbital-free kinetic-energy functionals. We prove that these models are linearly stable but nonlinearly unstable, in the sense that the corresponding kinetic-energy functionals are not bounded from below. As a matter of illustration, we provide an example of an electronic density of simple shape, the kinetic energy of which is negative. [ABSTRACT FROM AUTHOR]

In 1984 Boshernitzan proved an upper bound on the number of ergodic measures for a minimal subshift of linear block growth and asked if it could be lowered without further assumptions on the shift. We answer this question, showing that Boshernitzan's bound is sharp. We further prove that the same bound holds for the, a priori, larger set of nonatomic generic measures, and that this bound remains valid even if one drops the assumption of minimality. Applying these results to interval exchange transformations, we give an upper bound on the number of nonatomic generic measures of a minimal IET, answering a question recently posed by Chaika and Masur. [ABSTRACT FROM AUTHOR]

We prove a strong form of the quantitative Sobolev inequality in ℝ n for p ≥ 2, where the deficit of a function ∈ W¹,p controls //∇u-∇v//Lp for an extremal function v in the Sobolev inequality. [ABSTRACT FROM AUTHOR]

Characteristic p multizeta values were initially studied by Thakur, who defined them as analogues of classical multiple zeta values of Euler. In the present paper we establish an effective criterion for Eulerian multizeta values, which characterizes when a multizeta value is a rational multiple of a power of the Carlitz period. The resulting "t -motivic" algorithm can tell us whether any given multizeta value is Eulerian or not. We also prove that if ζA(s1,...,sr) is Eulerian, then ζA(s2,...,sr) has to be Eulerian. This was conjectured by Lara Rodríguez and Thakur for the zeta-like case from numerical data. Our methods apply equally well to values of Carlitz multiple polylogarithms at algebraic points and can also be extended to determine zeta-like multizeta values. [ABSTRACT FROM AUTHOR]

We apply the saddle–point‐type theorems of Rabinowitz and Benci‐Rabinowitz for local Lipschitz functionals that entails an extension of the classical Palais‐Smale‐Cerami condition for a C1 functional to this setting to show the existence of new periodic solutions for second‐order Hamiltonian systems with local Lipschitz potentials, which are weaker than Rabinowitz's original conditions. The key difficulty in these arguments arises from the lack of smoothness and symmetry in the potential when extending the Cerami‐Palais‐Smale condition for the local Lipschitz case. [ABSTRACT FROM AUTHOR]

Abstract In this paper we study optimal estimates for two functionals involving the anisotropic p -torsional rigidity T p (Ω) , 1 < p < + ∞. More precisely, we study Φ (Ω) = T p (Ω) | Ω | M (Ω) and Ψ (Ω) = T p (Ω) | Ω | [ R F (Ω) ] p p − 1 , where M (Ω) is the maximum of the torsion function u Ω and R F (Ω) is the anisotropic inradius of Ω. [ABSTRACT FROM AUTHOR]

Motivated by the formula, due to Bourgain, Brezis and Mironescu, lim 𝜖 → 0 + ∫ Ω ∫ Ω | u (x) − u (y) | q | x − y | q ρ 𝜖 (x − y) d x d y = K q , N ∥ ∇ u ∥ L q q , that characterizes the functions in L q that belong to W 1 , q (for q > 1) and B V (for q = 1), respectively, we study what happens when one replaces the denominator in the expression above by | x − y |. It turns out that for q > 1 the corresponding functionals "see" only the jumps of the B V function. We further identify the function space relevant to the study of these functionals, the space B V q , as the Besov space B q , ∞ 1 / q . We show, among other things, that B V q (Ω) contains both the spaces B V (Ω) ∩ L ∞ (Ω) and W 1 / q , q (Ω). We also present applications to the study of singular perturbation problems of Aviles–Giga type. [ABSTRACT FROM AUTHOR]

In this paper, we study a general class of nonlinear anisotrpic elliptic problems associated with the differential inclusion β(u) − div(a(x, D(u) + F(u)) 3 f in Ω, where f ∈ L∞(Ω). A vector field a(., .) is a Carath´eodory function. Using trunction techniques and the generalized monotonicity method in the functional spaces we prove the existence of renormalized solutions for L∞ − data. [ABSTRACT FROM AUTHOR]

We provide with a simple and explicit construction of a function in the disc algebra, whose derivatives enjoy a disjoint universal property near the boundary. The set of functions with such property is topologically generic, densely lineable, and spaceable. [ABSTRACT FROM AUTHOR]

For a Tychonoff space X , we denote by C p ( X ) the space of all real-valued continuous functions on X with the topology of pointwise convergence. In this paper we continue to study different selectors for sequences of dense sets of C p ( X ) started to study in the paper [14] . A set A ⊆ C p ( X ) will be called 1 -dense in C p ( X ) , if for each x ∈ X and an open set W in R there is f ∈ A such that f ( x ) ∈ W . We give the characterizations of selection principles S 1 ( A , A ) , S f i n ( A , A ) and S 1 ( S , A ) where • A — the family of 1-dense subsets of C p ( X ) ; • S — the family of sequentially dense subsets of C p ( X ) , through the selection principles of a space X . In particular, we give the functional characterizations of the Rothberger and Menger properties. [ABSTRACT FROM AUTHOR]

Following the ideas of our previous research, in this paper we continue the study of new Bergman-type spaces on the unit disc with mixed norm in terms of Fourier coefficients. Here we deal with the case where the sequence of norms of Fourier coefficients in the Orlicz–Morrey space in radial variable belongs to l q {l^{q}}. We study the boundedness of the Bergman projection and provide a description of functions in these spaces via the behavior of their Taylor coefficients. [ABSTRACT FROM AUTHOR]

For the problem of nonparametric regression of smooth functions, we reconsider and analyze a constrained variational approach, which we call the MultIscale Nemirovski--Dantzig (MIND) estimator. This can be viewed as a multiscale extension of the Dantzig selector (Ann. Statist. 35 (2009) 2313-2351) based on early ideas of Nemirovski (J. Comput. System Sci. 23 (1986) 1- 11). MIND minimizes a homogeneous Sobolev norm under the constraint that the multiresolution norm of the residual is bounded by a universal threshold. The main contribution of this paper is the derivation of convergence rates of MIND with respect to Lq - loss, 1 ≤ q ≤∞, both almost surely and in expectation. To this end, we introduce the method of approximate source conditions. For a one-dimensional signal, these can be translated into approximation properties of B-splines. A remarkable consequence is that MIND attains almost minimax optimal rates simultaneously for a large range of Sobolev and Besov classes, which provides certain adaptation. Complimentary to the asymptotic analysis, we examine the finite sample performance of MIND by numerical simulations. A MATLAB package is available online. [ABSTRACT FROM AUTHOR]

The first aim of this paper is to give different necessary and sufficient conditions that guarantee the density of the set of compactly supported functions into the Sobolev space of order one in infinite p-adic weighted trees. The second goal is to define properly a trace operator in this Sobolev space if it makes sense. [ABSTRACT FROM AUTHOR]

Let X be a pointed metric space and let Lip0(X) be the space of all scalar-valued Lipschitz functions on X which vanish at the base point. We prove that Lip0(X) with the bounded weak* topology τbw* has the approximation property if and only if the Lipschitz-free Banach space F(X) has the approximation property if and only if, for each Banach space F, each Lipschitz operator from X into F can be approximated by Lipschitz finite-rank operators within the unique locally convex topology γτγ on Lip0(X, F) such that the Lipschitz transpose mapping f → ft is a topological isomorphism from (Lip0(X, F), γτγ) to (Lip0(X), τbw* )∈F. [ABSTRACT FROM AUTHOR]

The main purpose of the paper is to show that differentiability properties of a measurable function defined in the euclidean space can be described using square functions which involve its second symmetric di- vided differences. Classical results of Marcinkiewicz, Stein and Zygmund describe, up to sets of Lebesgue measure zero, the set of points where a function f is differentiable in terms of a certain square function g(f). It is natural to ask for the behavior of the divided differences at the complement of this set, that is, on the set of points where f is not differentiable. In the nineties, Anderson and Pitt proved that the growth of the divided differences of a function in the Zygmund class obeys a version of the classical Kolmogorov's Law of the Iterated Logarithm (LIL). A square function, which is the conical analogue of g(f) will be used to state and prove a general version of the LIL of Anderson and Pitt as well as to prove analogues of the classical results of Marcinkiewicz, Stein and Zygmund. Sobolev spaces can also be described using this new square function. [ABSTRACT FROM AUTHOR]

In this paper, we study the minimizing problem ... where ... N and ... is the Hardy- Littlewood-Sobolev upper critical exponent. Firstly, by using refinement of the Hardy- Littlewood-Sobolev inequality, we prove that Sp,1,α,μ is achieved in RN by a radially symmetric, nonincreasing and nonnegative function. Secondly, we give a estimation of extremal function. [ABSTRACT FROM AUTHOR]

Necessary and sufficient conditions in terms of lower cut sets are given for the strong insertion of a perfectly continuous function between two comparable real-valued functions on such topological spaces that ⋀sets are open. [ABSTRACT FROM AUTHOR]

In a domain obtained as a Cartesian product of an interval [0 ,T] and the space ℝ , p ∈ ℕ , for a system of equations (with constant coefficients) unsolved with respect to the highest time derivative, we study the problem with integral conditions in the time variable for a class of functions almost periodic in the space variables. A criterion of uniqueness and sufficient conditions for the existence of solution of this problem in different functional spaces are established. We use the metric approach to solve the problem of small denominators encountered in the construction of the solution. [ABSTRACT FROM AUTHOR]

Let (M, g) be a compact Riemannian surface without boundary, W1,2(M) be the usual Sobolev space, and J : W1,2(M) → R be the functional defined by J(u)= 1/2 ∫M/∇u/²dvg +8π∫Mudvg - 8π log ∫Mheudvg, where h is a positive smooth function on M. In an inspiring work (Asian J. Math., vol. 1, pp. 230-248, 1997), Ding, Jost, Li and Wang obtained a sufficient condition under which J achieves its minimum. In this note, we prove that if the smooth function h satisfies h ≥ 0 and h ≡ 0, then the above result still holds. Our method is to exclude blow-up points on the zero set of h. [ABSTRACT FROM AUTHOR]

We prove that many completeness properties coincide in metric spaces, precompact groups and dense subgroups of products of separable metric groups. We apply these results to function spaces C p ( X , G ) of G -valued continuous functions on a space X with the topology of pointwise convergence, for a separable metric group G . A space X is weakly pseudocompact if it is G δ -dense in at least one of its compactifications. A topological group G is precompact if it is topologically isomorphic to a subgroup of a compact group. We prove that every weakly pseudocompact precompact topological group is pseudocompact, thereby answering positively a question of M. Tkachenko. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonsmooth optimization problem with a convex feasible set described by constraint functions which are neither convex nor differentiable nor locally Lipschitz necessarily. Utilizing upper regular convexificators, we characterize the normal cone of the feasible set and derive KKT type necessary and sufficient optimality conditions. Under some assumptions, we show that the set of KKT multipliers is bounded. We also characterize the set of optimal solutions and introduce a linear approximation corresponding to the original problem which is useful in checking optimality. The obtained outcomes extend various results existing in the literature to a more general setting. [ABSTRACT FROM AUTHOR]

A GTS (X, μ) is said to be weakly μH-compact if for every μ-open cover {Vα : α ∈ ∆} of X there exists a finite subset ∆0 of ∆ such that X \ ∪{cμ(Vα) : α ∈ ∆0} ∈ H. In this paper we study the effect of functions on weakly μH-compact spaces. The main result is that the θ(μ, ν)-continuous image of a weakly μH-compact space is weakly νf(H)-compact. [ABSTRACT FROM AUTHOR]

We give a sufficient condition on strongly separately continuous function f to be continuous on space ℓp for p 2 [1;+1]. We prove the existence of an ssc function f : ℓ1 ! R which is not Baire measurable. We show that any open set in ℓp is the set of discontinuities of a strongly separately continuous real-valued function for p ∈ [1, +∞) [ABSTRACT FROM AUTHOR]

In this paper we study a sufficient conditions for continuous and θ α -continuous extensions of f to space X for an image space Y with different separation axioms. [ABSTRACT FROM AUTHOR]

In this paper, we give necessary and sufficient conditions for the space B 1 ( X ) of first Baire class functions on a Tychonoff space X , with pointwise topology, to be (strongly) sequentially separable. Also we claim that there are spaces X such that B 1 ( X ) is not sequentially separable space, but C p ( X ) is sequentially separable (the Sorgenfrey line, the Niemytzki plane). [ABSTRACT FROM AUTHOR]

Let D = {z ϵ C : ǀzǀ < 1g be the open unit disk, ' an analytic self-map of D and an analytic function on D. Let D be the differentiation operator and Wφψ the weighted composition operator. The boundedness and compactness of the product-type operators DWφψ from the weighted Bergman-Orlicz spaces to the Bloch-Orlicz spaces on D are characterized. [ABSTRACT FROM AUTHOR]

We give a sharp estimate for the codimension of the poly-Bergman space in the poly-Bergman space over the punctured domain. It is established the behaviour at the infinity point of polyanalytic Bergman functions on the complement of closed disks. In the main result of the paper, we prove that for [ABSTRACT FROM AUTHOR]

We prove that in finite dimensional spaces every ordered median function is the Minkowski dual of a reduced pair of polytopes. This implies a very general theorem on the representation of an ordered median function as a uniquely determined difference of two sublinear functions up to adding and subtracting one and the same arbitrary sublinear function. [ABSTRACT FROM AUTHOR]

In a domain specified in the form of the Cartesian product of an interval [0, T] and a space ℝ, we study a problem with integral conditions with respect to the time coordinate for Shilov parabolic systems of equations in the class of functions almost periodic with respect to the space variables. We establish a criterion of uniqueness and sufficient conditions for the existence of a solution of the problem. To solve the problem of small denominators encountered in the construction of the solution, we apply the metric approach. [ABSTRACT FROM AUTHOR]

Planar shape interpolation is a classic problem in computer graphics. We present a novel shape interpolation method that blends C&#8734; planar harmonic mappings represented in closed-form. The intermediate mappings in the blending are guaranteed to be locally injective C&#8734; harmonic mappings, with conformal and isometric distortion bounded by that of the input mappings. The key to the success of our method is the fact that the blended differentials of our interpolated mapping have a simple closed-form expression, so they can be evaluated with unprecedented efficiency and accuracy. Moreover, in contrast to previous approaches, these differentials are integrable, and result in an actual mapping without further modification. Our algorithm is embarrassingly parallel and is orders of magnitude faster than state-of-the-art methods due to its simplicity, yet it still produces mappings that are superior to those of existing techniques due to its guaranteed bounds on geometric distortion. [ABSTRACT FROM AUTHOR]

In this paper, the T b theorem of the inhomogeneous Besov and Triebel-Lizorkin spaces associated with a para-accretive function on homogeneous type spaces is established. As an application, we obtain that the Riesz potential can be used as the lifting operator of these spaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to discuss the construction of a linear operator, referred to as the bubble transform, which maps scalar functions defined on $${\varOmega }\subset \mathbb {R}^n$$ into a collection of functions with local support. In fact, for a given simplicial triangulation $${\fancyscript{T}}$$ of $${\varOmega }$$ , the associated bubble transform $${\fancyscript{B}}_{{\fancyscript{T}}}$$ produces a decomposition of functions on $${\varOmega }$$ into a sum of functions with support on the corresponding macroelements. The transform is bounded in both $$L^2$$ and the Sobolev space $$H^1$$ , it is local, and it preserves the corresponding continuous piecewise polynomial spaces. As a consequence, this transform is a useful tool for constructing local projection operators into finite element spaces such that the appropriate operator norms are bounded independently of polynomial degree. The transform is basically constructed by two families of operators, local averaging operators and rational trace preserving cutoff operators. [ABSTRACT FROM AUTHOR]

We prove that the class of the classifying stack BPGLn is the multiplicative inverse of the class of the projective linear group PGLn in the Grothendieck ring of stacks K0(Stackk) for n = 2 and n = 3 under mild conditions on the base field k. In particular, although it is known that the multiplicativity relation {T} = {S} · {PGLn} does not hold for all PGLn-torsors T → S, it holds for the universal PGLn-torsors for said n. [ABSTRACT FROM AUTHOR]

For Hölder cocycles over a Lipschitz base transformation, possibly non-invertible, we show that the subbundles given by the Oseledets Theorem are Hölder-continuous on compact sets of measure arbitrarily close to 1. The results extend to vector bundle automorphisms, as well as to the Kontsevich-Zorich cocycle over the Teichmüller flow on the moduli space of abelian differentials. Following a recent result of Chaika-Eskin, our results also extend to any given Teichmüller disk. [ABSTRACT FROM AUTHOR]

We show that the category of finitely generated free modules over certain local rings is nangulated for every n ⩾ 3. In fact, we construct several classes of n-angles, parameterized by equivalence classes of units in the local rings. Finally, we show that for odd values of n some of these n-angulated categories are not algebraic. [ABSTRACT FROM AUTHOR]

Let (X, τ, I) be an ideal topological space. For a subset A of X, a local function Γ*(A)(I, τ) is defined as follows: Γ*(A)(I, τ) = {x ϵ X : A ∩ Cl(U) ∉ I for every regular open set U containing xg. This coincides with the δ-local functions due to Hatir et al. [2]. By using Γ*(A)(I, τ ), an operator ΨΓ* : P(X) →τδ is de-ned as the dual of the δ-local function and its relations with δ-codense ideals are investigated. [ABSTRACT FROM AUTHOR]

We derive several univalent and p-valent conditions on certain meromorphic functions by applying well-known Nunokawa’s lemmas. [ABSTRACT FROM AUTHOR]

Nonsmooth nonconvex optimization models have been widely used in the restoration and reconstruction of real images. In this paper, we consider a linearly constrained optimization problem with a non-Lipschitz regularization term in the objective function which includes the lp norm (0 < p < 1) of the gradient of the underlying image in the l2-lp problem as a special case. We prove that any cluster point of ϵ scaled first order stationary points satisfies a first order necessary condition for a local minimizer of the optimization problem as ϵ goes to 0. We propose a smoothing quadratic regularization (SQR) method for solving the problem. At each iteration of the SQR algorithm, a new iterate is generated by solving a strongly convex quadratic problem with linear constraints. Moreover, we show that the SQR algorithm can find an ϵ scaled first order stationary point in at most O(ϵ-2) iterations from any starting point. Numerical examples are given to show good performance of the SQR algorithm for image restoration. [ABSTRACT FROM AUTHOR]