Nervous Children. By Beverly R. Tucker, M.D. Boston: Richard G. Badger, 1916. Pp. 147. Dr. Tucker writes as a neurologist, but not for neurologists. What strikes most forcibly a student of psychology is his apparent failure to grasp the psychological problems of nervous and mentally deficient children, and his lack of any reference to the large and growing psychological literature on their trai...

This paper is devoted to studying the robust isolated calmness of the Karush– Kuhn–Tucker (KKT) solution mapping for a large class of interesting conic programming problems (including most commonly known ones arising from applications) at a locally optimal solution. Under the Robinson constraint qualification, we show that the KKT solution mapping is robustly isolated calm if and only if both t...

We report on the use of a quadratic programming technique in recent and upcoming spectrum auctions in Europe. Specifically, we compute a unique point in the core that minimizes the sum of squared deviations from a reference point, for example, from the Vickrey-Clarke-Groves payments. Analyzing the Karush-Kuhn-Tucker conditions, we demonstrate that the resulting payments can be decomposed into a...

Motivated by the Maximum Theorem for convex functions (in setting of linear spaces) and subadditive Abelian semigroups), we establish a class generalized functions, i.e., $f:X\to\R$ that satisfy inequality $f(x\circ y)\leq pf(x)+qf(y)$, where $\circ$ is binary operation on $X$ $p,q$ are positive constants. As an application, also obtain extension Karush--Kuhn--Tucker theorem this functions.

In this paper, Karush-Kuhn-Tucker type robust necessary optimality conditions for a nonsmooth interval-valued optimization problem (UCIVOP) are formulated using the concept of LU-optimal solution and generalized Slater constraint qualification (GRSCQ). These shown to be sufficient under convexity. The Wolfe Mond-Weir dual problems over cones convexity assumptions, usual duality results establis...

This paper is concerned with the numerical solution of a Karush–Kuhn– Tucker system. Such symmetric indefinite system arises when we solve a nonlinear programming problem by an Interior–Point (IP) approach. In this framework, we discuss the effectiveness of two inner iterative solvers: the method of multipliers and the preconditioned conjugate gradient method. We discuss the implementation deta...

We describe a primal-dual interior point algorithm for convex quadratic programming problems which requires a total of O(~/nL) number of iterations, where L is the input size. Each iteration updates a penalty parameter and finds an approximate Newton direction associated with the Karush-Kuhn-Tucker system of equations which characterizes a solution of the logarithmic barrier function problem. T...

In this article, we consider the network utility maximization (NUM) problem for the random access network with multiclass traffic. The utilities associated with the users are not only concave, but also nonconcave functions. Consequently, the random access NUM problem becomes more difficult to solve. Based on the successive approximation method, we propose an algorithm that jointly controls the ...

Blur in images can be removed by solving a series of box-constrained least-squares problems. In this paper, we compare two recent approaches for solving these problems using affine-scaling methods. Both approaches aim at solving a nonlinear system arising from the Karush-Kuhn-Tucker condition. One approach is to identify the active set and update the inactive components of the iterates by using...

A few Karush-Kuhn-Tucker type of sufficient optimality conditions are given in this paper for nonsmooth continuous-time nonlinear multi-objective optimization problems in the Banach space L∞ [0, T ] of all n-dimensional vector-valued Lebesgue measurable functions which are essentially bounded, using Clarke regularity and generalized convexity. Further, we establish duality theorems for Wolfe an...