集值映射向量优化的一个必要条件

本文在局部凸拓扑向量空间中得到了如下集值映射向量优化：ｍｉｎＦ（ｘ）ｓ．ｔ．Ｇ（ｘ）(（－Ｋ_１）,０∈Ｈ（ｘ）的必要条件即 Ｆｒｉｔｚ Ｊｏｈｎ条件．     

The added mass for two-dimensional floating structures

The diagonal terms in the added mass matrix for a two-dimensional surface-piercing structure, which satisfies a geometric condition known as the John condition, are proven to be non-negative. It is also shown that the heave coefficient, associated with a symmetric system of two such structures, is non-negative when the length of the free surface connecting the structures lies between an odd, and the next higher even, number of half-wavelengths. The sway and roll coefficients, associated with antisymmetric motion of the system, are non-negative in the complementary intervals. For a specific geometry these intervals are equivalent to frequency ranges. Negative added mass is associated with rapid variations with frequency, due to complex resonances that correspond to simple poles of the associated radiation potential in the complex frequency domain. Approximate techniques are used to show that, for systems of two structures, complex resonances are located at frequencies consistent with the intervals in which negative added mass is able to occur.     

A generalized karush-kuhn-tucki optimality condition without constraint qualification using tl approximate subdifferential

A generalized Karush-Kuhn-Tucker first order optimality condition is established for an abstract cone-constrained programming problem involving locally Lipschitz functions using the approximate subdifferential. This result is obtained without recourse to a constraint qualification by imposing additional generalized convexity conditions on the constraint functions. A new Fritz John optimality condition is developed as a precursor to the main result. Several examples are provided to illustrate the results along with a discussion of applications to concave minimization problems and to stochastic programming problems with nonsmooth data.     

Weighted bounded mean oscillation applied to backward stochastic differential equations

We deduce conditional $L_p$-estimates for the variation of a solution of a BSDE. Both quadratic and sub-quadratic types of BSDEs are considered, and using the theory of weighted bounded mean oscillation we deduce new tail estimates for the solution $(Y,Z)$ on subintervals of $[0,T]$. Some new results for the decoupling technique introduced in Geiss and Ylinen (2019) are obtained as well and some applications of the tail estimates are given.     

Optimality for nonsmooth fractional multiple objective programming

In this study the necessary and sufficient optimality conditions for nonsmooth fractional multiple objective optimization problems are provided. Our idea is based on using the properties of limiting subdifferential vectors in nonsmooth analysis and a separation theorem in convex analysis.     

关于新几何体Γ_(-p)K的几个不等式

本文研究了新几何体Γ_(-p)K与L_p-质心体和L_p-John椭球有关的几个有趣不等式,包括L_p-Busemann-Petty质心不等式的一种隔离,同时探讨了新几何体Γ_(-p)K的单调性．     

FJ-Invex control problem

This paper introduces a new condition on the functionals of a control problem and extends a recent characterization result of KT-invexity. We prove that the new condition, the FJ-invexity, is both necessary and sufficient in order to characterize the optimal solution set using Fritz John points.     

A Conversation with Robert F. Christy – Part II

Robert F. Christy, Institute Professor of Theoretical Physics Emeritus at Caltech, recalls his wartime work at Los Alamos on the critical assembly for the plutonium bomb (“the Christy bomb”); the Alamogordo test, July 16, 1945; the postwar concerns of ALAS (Association of Los Alamos Scientists); his brief return to the University of Chicago and move to Caltech; friendship with and later alienation from Edward Teller; work with Charles and Tommy Lauritsen and William A. Fowler in Caltech’s Kellogg Radiation Laboratory; Freeman Dyson’s Orion Project; work on the meson and RR Lyrae stars; fellowship at Cambridge University; 1950s Vista Project at Caltech; his opposition to the Strategic Defense Initiative; and his post-retirement work for the National Research Council’s Committee on Dosimetry and on inertial-confinement fusion.