Resolving Singularities in a Ramsey-type Growth Model

The aim of this paper is to discuss a mathematical solution procedure to solve a Ramsay-type growth model that explains the fundamentals of consumption and capital accumula-tion in a dynamic equilibrium setting. The problem is formulated as a system of recursive equations and studied through some numerical experiments for the time path of the different variables of the model under some alternative assumption for the steady-state equilibrium of the labour market conditioning the possible singularity of the model.     

Applications of Variational Analysis to a Generalized Fermat-Torricelli Problem

In this paper we develop new applications of variational analysis and generalized differentiation to the following optimization problem and its specifications: given n closed subsets of a Banach space, find such a point for which the sum of its distances to these sets is minimal. This problem can be viewed as an extension of the celebrated Fermat-Torricelli problem: given three points on the plane, find another point that minimizes the sum of its distances to the designated points. The generalized Fermat-Torricelli problem formulated and studied in this paper is of undoubted mathematical interest and is promising for various applications including those frequently arising in location science, optimal networks, etc. Based on advanced tools and recent results of variational analysis and generalized differentiation, we derive necessary as well as necessary and sufficient optimality conditions for the extended version of the Fermat-Torricelli problem under consideration, which allow us to completely solve it in some important settings. Furthermore, we develop and justify a numerical algorithm of the subgradient type to find optimal solutions in convex settings and provide its numerical implementations.     

New Approach to Solving a System of Variational Inequalities and Hierarchical Problems

This paper deals with a viscosity iterative method, in real Hilbert spaces, for solving a system of variational inequalities over the fixed-point sets of possibly discontinuous mappings. Under classical conditions, we prove a strong convergence theorem for our method. The proposed algorithm can be applied for instance to solving variational inequalities in some situations when the projection methods fail. Moreover, the techniques of analysis are novel and provide new tools in designing approximation schemes for combined and bilevel optimization problems.     

声波方程波速奇性一体化成象

本文利用-体化算子,给出了-种求找波速奇性间断的方法.利用G.Beylkin的思想将一Fourier积分算子分解成-体化成像算子与-体化算子之积,然后由拟微分算子的渐近展开,将其表示为一小波算子与一紧箅子之和,从而获得波速奇性位于-体化成象算子最大模点处的结论.利用二层介质一维波速场对以上结论进行了验证.     

Variational Inequalities and Applications to a Continuum Model of Transportation Network with Capacity Constraints

A continuum model of transportation network is considered in presence of capacity constraints on the flow. The equilibrium conditions are expressed in terms of a Variational Inequality for which an existence theorem is provided.     

具有张弛粘弹性模型的整体光滑可解性及奇性形成

考虑了具有张弛粘弹性模型Ｃａｕｃｈｙ 问题的整体光滑可解性及解的奇性形成     

Preface to Variational Analysis for Beginners

Set-Valued and Variational Analysis -     

Transversality in Variational Analysis

We discuss various aspects of newly developed extension of the classical transversality theory to variational analysis and optimization theory. In particular, we give interpretations in transversality terms of some key results (relating to subdifferential calculus, necessary optimality conditions and linear convergence of alternating projections) and prove a set-valued version of the Thom transversality theorem for semi-algebraic objects.     

参数变分不等式的灵敏性分析

本文在所给函数和映射均不可微的前提下，通过建立参数变分不等式和参数Wiener-Hopf方程的等价性，分析了Hilbert空间中参数变分不等式的局部唯一解的灵敏性。文中所用方法是N.D.Yen之方法的改进，使用这一方法可大大简化N.D.Yen一文中主要结果（引理2.1)的证明。     

On a New Class of Vector Variational Control Problems

Abstract

In this paper, we introduce geodesic (strongly) b-V-KT-pseudoinvex multidimensional control problems. This new class of multiobjective variational control problems, involving multiple integral cost functionals, is described such that every geodesic Kuhn–Tucker point is geodesic efficient solution. In addition, to illustrate the effectiveness of our main result, the paper is completed with an application.     

A New Class of Monotone Mappings and a New Class of Variational Inclusions in Banach Spaces

In this paper, we introduce and study a new class of variational inclusions in Banach spaces. As it concerns the methods of solution, we introduce a new class of monotone mappings. We define a proximal mapping associated with this mappings and show its Lipschitz continuity. By using the technique of proximal mapping, we construct a new iterative algorithm. Under some suitable conditions, we prove the convergence of iterative sequences generated by the algorithm. Our results improve and generalize many known results.     

Topics on Variational Analysis and Applications to Equilibrium Problems

We observe how many equilibrium problems obey a generalized complementarity condition, which in general leads to a variational inequality. We illustrate this fact, by studying the elastic–plastic torsion problem and finding the related Lagrange multipliers.     

Variational Methods in Convex Analysis

We use variational methods to provide a concise development of a number of basic results in convex and functional analysis. This illuminates the parallels between convex analysis and smooth subdifferential theory. Research was supported by NSERC and by the Canada Research Chair Program and National Science Foundation under grant DMS 0102496.     

On the Existence of Focus Singularities in One Model of a Lagrange Top with a Vibrating Suspension Point

Doklady Mathematics - We consider a completely integrable Hamiltonian system with two degrees of freedom that describes the dynamics of a Lagrange top with a vibrating suspension point. The results...     

Variational Analysis and Generalized Equations in Electronics

The paper is devoted to the study of the Aubin/Lipschitz-like property and the isolated calmness of a particular non-monotone generalized equation arising in electronics. The variational and non-smooth analysis is applied in the theory of non-regular electrical circuits involving electronic devices like ideal diodes, practical diodes, DIACs, silicon controlled rectifiers (SCR), and transistors. We also discuss the relationship of our results to the ones using classical techniques from (smooth) analysis and provide a simulation for several simple electrical circuits which are chosen in order to cover the most common non-smooth elements in electronics. The simulations of the electrical circuits discussed in this paper are performed by using Xcos (a component of Scilab).     

Singularities of the envelope of curves tangent to a semi-cubic cusp

We study the envelope of one-parameter families of smooth curves tangent to a curve having a semi-cubic cusp such that the radius of curvature at the tangency point vanishes when this point approaches the cusp. We show that, in general, the closure of the envelope has two semi-cubic cusps at the same point, one of which is the given cusp tangent to the same straight line. We study also nongeneric and dual cases and normal forms of the equation of the envelope.Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 7, Suzdal Conference-1, 2003.This revised version was published online in April 2005 with a corrected cover date.