Pseudo Convex Research Articles

Approximate solutions for robust multiobjective optimization programming in Asplund spaces

In this paper, we study a nonsmooth/nonconvex multiobjective optimization problem with uncertain constraints in arbitrary Asplund spaces. We first provide necessary optimality condition in a fuzzy form for approximate weakly robust efficient solutions and then establish necessary optimality theorem for approximate weakly robust quasi-efficient solutions of the problem in the sense of the limiting subdifferential by exploiting a fuzzy optimality condition in terms of the Fréchet subdifferential. Sufficient conditions for approximate (weakly) robust quasi-efficient solutions to such a problem are also driven under the new concept of generalized pseudo convex functions. Finally, we address an approximate Mond-Weir-type dual robust problem to the reference problem and explore weak, strong, and converse duality properties under assumptions of pseudo convexity.

Morrey boundedness and compactness characterizations of integral commutators with singular kernel on strictly pseudoconvex domains in [formula omitted

We prove the Morrey boundedness and compactness characterization of integral commutators with singular kernel of Calderón-Zygmund type on pseudo convex domains in Cn. Our results extend some of the ones of Krantz-Li in [16,17].

Pseudo Convex Framework using Sparse Channel Estimation for Multipath Fading Channels in DS-CDMA Systems

A Direct-Sequence Code-Division Multiple-Access (DS-CDMA) with rake receiver for multiuser system sets up a new dimension in mobile communication system. We propose a pseudo convex framework using an optimum sparse channel estimation technique for DS-CDMA mobile communication systems. Further, the blind channel estimation problem will be examined for rake-based DS-CDMA communication framework with time variant multi-path fading channels This receiver accomplishes an effective assessment of channel according to a maximum convexity criterion, by means of the sparse technique. This estimation method requires a convenient representation of the discrete multipath fading channel based on the sparse theory. In this paper, we have defined a specialized interior-point method for solving large-scale ℓ1 - problem in multiuser detection. Our method can be generalized to handle a variety of extensions such as various channel conditions. A new solution to DS-CDMA based sparse channel estimation is presented in this paper that assures a global optimal solution. Also, it is proven that the said solution can be used as an apparent program that shall enable solutions utilizing interior point techniques involving polynomial time complexity. Through simulation the rationality of the techniques proposed in this paper has been highlighted by results obtained for various modulation schemes and channel parameters. The execution of a pseudo convex framework using sparse channel estimation technique with rake receiver in DS-CDMA framework for multipath fading channels is explored. The overall performance is evaluated in terms of bit error rate (BER) for a range of values of signal to noise ratio (SNR). This framework gives better performance under various modulation schemes using pseudo noise (PN) spreading code. Furthermore, performance of the proposed system is compared with different detectors.

Global Connecting Dual Representation of Non-Smooth Multi-Objective Programs using Convex Functions

New classes of vector functions ,namely V-(𝒃 , 𝑭 , 𝝆 )- pseudo convex and V- (𝒃 , 𝑭 , 𝝆 )- quasi convex functions are introduced which are weaker than V-(𝒃, 𝑭 , 𝝆 )- convex functions. Sufficient optimality conditions for proper potency and numerous duality theorems for a category of nonsmooth multiobjective programs are obtained under the assumptions of the above said functions.

The Raising Steps Method: Applications to the $$\bar{\partial }$$ ∂ ¯ Equation in Stein Manifolds

In order to have estimates on the solutions of the equation $$\bar{\partial }u=\omega $$ on a Stein manifold, we introduce a new method, the “raising steps method”, to get global results from local ones. In particular, it allows us to transfer results from open sets in $${\mathbb {C}}^{n}$$ to open sets in a Stein manifold. Using it, we get $$\displaystyle L^{r}-L^{s}$$ results for solutions of the equation $$\bar{\partial }u=\omega $$ with a gain, $$\displaystyle s>r$$ , in strictly pseudo convex domains in Stein manifolds. We also get $$\displaystyle L^{r}-L^{s}$$ results for domains in $${\mathbb {C}}^{n}$$ locally biholomorphic to convex domains of finite type.

Optimality Criteria for Fuzzy Pseudo Convex Functions

Convex optimization can provide both global as well as local solution; in the case of non convex optimization, it is difficult to get global solution. This paper presents some optimality criteria for the non convex programming problem whose objective function is fuzzy pseudo convex functions.

On some characterizations of preinvex fuzzy mappings

Jeyakumar (Methods Oper. Res. 55:109–125, 1985) and Weir and Mond (J. Math. Anal. Appl. 136:29–38, 1988) introduced the concept of preinvex function. The preinvex functions have some interesting properties. For example, every local minimum of a preinvex function is a global minimum and nonnegative linear combinations of preinvex functions are preinvex. Invex functions were introduced by Hanson (J. Math. Anal. Appl. 80:545–550, 1981) as a generalization of differentiable convex functions. These functions are more general than the convex and pseudo convex ones. The type of invex function is equivalent to the type of function whose stationary points are global minima. Under some conditions, an invex function is also a preinvex function. Syau (Fuzzy Sets Syst. 115:455–461, 2000) introduced the concepts of pseudoconvexity, invexity, and pseudoinvexity for fuzzy mappings of one variable by using the notion of differentiability and the results proposed by Goestschel and Voxman (Fuzzy Sets Syst. 18:31–43, 1986). Wu and Xu (Fuzzy Sets Syst 159:2090–2103, 2008) introduced the concepts of fuzzy pseudoconvex, fuzzy invex, fuzzy pseudoinvex, and fuzzy preinvex mapping from Rn to the set of fuzzy numbers based on the concept of differentiability of fuzzy mapping defined by Wang and Wu (Fuzzy Sets Syst. 138:559–591, 2003). In this paper, we present some characterizations of preinvex fuzzy mappings. The necessary and sufficient conditions for differentiable and twice differentiable preinvex fuzzy mapping are provided. These characterizations correct and improve previous results given by other authors. This fact is shown with examples. Moreover, we introduce additional conditions under which these results are valid.

An integrated vendor‐buyer inventory model with partial backordering

PurposeThe purpose of this paper is to analyze the effects of supply chain coordination on inventory management while the retailer inventory cycle consists of a shortage period and the backorder rate linearly decreases as a function of shortage duration. It is intended to consider how on‐hand inventory and shortage durations are altered when the decisions are centralized.Design/methodology/approachMathematical modelling of inventory costs for the retailer and the vendor is used to formulate objective functions. The vendor sets his inventory period as an integer multiple (n) of the retailer inventory cycle in which the integer multiple is a decision variable. Solution spaces of models are analyzed to determine two other decision variables including, on‐hand inventory duration and shortage length.FindingsThe integrated model consists of a unique pseudo convex area when (n) is fixed and as a result, there is a unique minimum point. Based on numerical examples and sensitivity analysis, in most situations coordinated inventory management reduces total costs of the supply chain and cost reduction rate increase at larger production rates.Originality/valueThis paper is a combination between production‐inventory models in two‐stage supply chains and partial backordering, which has appeared in single inventory models. To the best of the authors' knowledge, no mathematical model has yet been proposed. Moreover, the benefits of synchronization are analyzed through numerical examples.

HOLOMORPHIC LIFTINGS FROM INFINITE DIMENSIONAL SPACES

We obtain a number of positive solutions to the following problem: if is a domain in a locally convex space E, X and Y axe Banach spaces with Y C X and quotient mapping n : X —> X/Y, and / : f2 —» X/Y is holomorphic, does there exist a holomorphic mapping h : ft —» X such that / = 7r o h'i The mapping h is called a (holomorphic) lifting. For example, we obtain a positive result when Si is pseudo convex, E is a Banach space with an unconditional basis and Y is an M-ideal in X.

Higher order duality in vector optimization over cones

In this paper higher order cone convex, pseudo convex, strongly pseudo convex, and quasiconvex functions are introduced. Higher order sufficient optimality conditions are given for a weak minimum, minimum, strong minimum and Benson proper minimum solution of a vector optimization problem. A higher order dual is associated and weak and strong duality results are established under these new generalized convexity assumptions.

Hilbert-Schmidt Hankel Operators and Berezin Iteration

Let $H$ be a reproducing kernel Hilbert space contained in a wider space $L^2(X,\mu)$. We study the Hilbert-Schmidt property of Hankel operators $H_g$ on $H$ with bounded symbol $g$ by analyzing the behavior of the iterated Berezin transform. We determine symbol classes $\mathcal{S}$ such that for $g\in \mathcal{S}$ the Hilbert-Schmidt property of $H_g$ implies that $H_{\bar{g}}$ is a Hilbert-Schmidt operator as well and there is a norm estimate of the form $\|H_{\bar{g}}\|_{\text{HS}}\leq C\cdot \| H_g\|_{\text{HS}}$. Finally, applications to the case of Bergman spaces over strictly pseudo convex domains in $\mathbb{C}^n$, the Fock space, the pluri-harmonic Fock space and spaces of holomorphic functions on a quadric are given.

The Hamiltonian dynamics over real hypersurfaces in Kaehler manifolds

Let X be a Kaehler manifold with complex dimension n. Let ω X be its Kaehler form. Let M be a strongly pseudo convex real hypersurface in X. For this hypersurface, the deformation theory of CR structures is successfully developed. And we find that H 1 ( M , T ′ ) (the T ′ -valued Kohn–Rossi cohomology) is the Zariski tangent space of the versal family. In this paper, the geometrical meaning of H 1 ( M , O ) is studied, and we propose to study displacements of the real hypersurface, which preserves the type of the differential form, ω X , over CR structures, on M, infinitesimally.

The canonical Kaehler potential on the parameter space of the versal family of CR structures

Let ( M, 0 T″) be a compact strongly pseudo convex CR structure with dim R M=2 n−1. Then, in [Michigan Math. J. 50 (2002) 517–549], the construction of the versal family of CR structures is settled. The purpose of this paper is to introduce a canonical Kaehler metric for the parameter space of this versal family if the CR structure admits a normal vector field and a non-vanishing CR n-form with the condition H 1(M, O M)=0 and H 1 M,∧ n−1(T′) ∗ ≃Z 1, where Z 1 is introduced in [Compositio Math. 85 (1993) 57–85].

Addendum to "Extremal discs and the regularity of CR mappings in higher codimension"

We give a proof of the regularity of Hölder CR homeomorphisms of strictly pseudo convex CR manifolds of higher codimension.

SOLVING PSEUDO-CONVEX MIXED INTEGER OPTIMIZATION PROBLEMS BY CUTTING PLANE TECHNIQUES

In the present paper a cutting plane approach to solve mixed-integer non-linear programming (MINLP) problems, containing pseudo-convex functions, is given. It is shown how valid cutting planes for pseudo convex functions can be obtained and, furthermore, it is shown how a class of non-convex MINLP problems with a pseudo-convex objective function and pseudo-convex constraints, can be solved to global optimality with the considered cutting plane technique. Finally the numerical efficiency of the procedure, when solving some example problems, is illustrated.

On harmonic functions operating in locally {$m$}-pseudo convex algebras

On harmonic functions operating in locally {$m$}-pseudo convex algebras

THE BOCHNER TYPE CURVATURE TENSOR OF PSEUDO CONVEX CR-STRUCTURES

For a pseudo-convex CR-structure on an odd dimensional manifold, we introduce a family of canonical torsion-free linear connections. Every connection in this family is uniquely determined by an almost contact structure associated with the given pseudo convex CR-structure. We study the change of the connections in this family under the gauge transformations and, accordingly, the corresponding change of the gauge tensor fields. The Bochner type curvature tensor field we get is invariant under gauge transformations.

On the Kuranishi family of deformations of complex structures over a tubular neighborhood of a strongly pseudo convex boundary with complex dimension 3.

Article On the Kuranishi family of deformations of complex structures over a tubular neighborhood of a strongly pseudo convex boundary with complex dimension 3. was published on January 1, 1992 in the journal Journal für die reine und angewandte Mathematik (volume 1992, issue 433).

A Criterion for Versality Of Deformations of Tubular Neighborhoods of Strongly Pseudo Convex Boundaries

AbstractWe extend the famous Kodaira-Spencer's completeness theorem for a family of deformations of complex structures (see [12]). As an application, we show that the canonical family constructed in [9] is versai.

Complex analytic construction of the Kuranishi family on a normal strongly pseudo convex manifold with real dimension 5

Complex analytic construction of the Kuranishi family on a normal strongly pseudo convex manifold with real dimension 5