An Algorithm for Strictly Convex Quadratic Programming with Box Constraints

1IntroductionWeconsiderastrictlyconvex(i.e.,positivedefinite)quadraticprogrammingproblemsubjecttoboxconstraints:t-iereA=[aij]isannxnsymmetricpositivedefinitematrix,andb,canddaren-vectors.Letg(x)bethegradient,Ax b,off(x)atx.Withoutlossofgeneralityweassumebothcianddiarefinitenumbers,ci相似文献   

Meromorphic Convex Functions with Negative Coefficients

Let σ_k(a) be the class of functions f(f)=1/z-sur from n=1 to ∞(|a_n|z~n), regular in the punctured disk E={z:0<|z|<1} and satisfying Re(1 zf"(z)/f'(z))<-a (0≤a<1) for z∈E. In this paper we obtain coefficient inequalities, distortion and closure Theorems for the class σ_k(a). Further we obtain the class preserving integral operator of the form     

Convex Approximation of Some Kind of Convex Functions

Suppose that f(x)∈C~2[0,1] is a convex function.we concern the approxi-mation degree of f(x)by convex algebraic Polynomials.Among the other things,it is a very important question whether we have convex polynomials of degree nsuch that     

Wavelet Approximation of Distributions with Bounded Variation Derivatives

Let BV ^r denote the space of distributions f such that the distributional derivatives D ^α f with |α|≤r exist as measures of bounded variation. This paper discusses estimates for wavelet coefficients of BV ^r distributions, direct (Jackson) and inverse (Bernstein) inequalities for n-term approximation of elements of BV ^r in the L _p spaces using compactly supported wavelets. In particular, optimal rates of approximation are established. Linear approximation in similar contexts is also considered for comparison. This research was supported by the 2003–2007 Academic Grant of Prof. P. Wojtaszczyk awarded by the Foundation for Polish Science. Part of this research was supported within the HASSIP framework.     

Convex Underestimation of Twice Continuously Differentiable Functions by Piecewise Quadratic Perturbation: Spline αBB Underestimators

This paper describes the construction of convex underestimators for twice continuously differentiable functions over box domains through piecewise quadratic perturbation functions. A refinement of the classical α BB convex underestimator, the underestimators derived through this approach may be significantly tighter than the classical αBB underestimator. The convex underestimator is the difference of the nonconvex function f and a smooth, piecewise quadratic, perturbation function, q. The convexity of the underestimator is guaranteed through an analysis of the eigenvalues of the Hessian of f over all subdomains of a partition of the original box domain. Smoothness properties of the piecewise quadratic perturbation function are derived in a manner analogous to that of spline construction.     

Duality of Unary Convex Functions Programming

Most nonliner programming problems consist of functions which are sums of unary,convexfunctions of linear fuctions.In this paper.we derive the duality forms of the unary oonvex optimization,and these technuqucs are applied to the geometric programming and minimum discrimination informationproblems.     

Bounded Perturbations of Second Order Ordinary Differential Equations

In the studying of the non-dissipative systems,the following periodic boundaryvalue problemsplay a very important role.where p(t)is 2 π-periodic and continuous,g∈C'(R),xg(x)>0(x≠0).Some existence results were obtained under various additional as-     

Some Further Generalizations of Ostrowski Inequality for Hölder Functions and Functions with Bounded Derivatives

Some generalizations of Ostrowski inequality for Hölder functions and functions with bounded derivatives are given.     

Ergodic Type Bellman Equations of First Order with Quadratic Hamiltonian

We consider Bellman equations of ergodic type in first order. The Hamiltonian is quadratic on the first derivative of the solution. We study the structure of viscosity solutions and show that there exists a critical value among the solutions. It is proved that the critical value has the representation by the long time average of the kernel of the max-plus Schrödinger type semigroup. We also characterize the critical value in terms of an invariant density in max-plus sense, which can be understood as a counterpart of the characterization of the principal eigenvalue of the Schrödinger operator by an invariant measure.     

Optimization and Variational Inequalities with Pseudoconvex Functions

In the present paper we consider a pseudoconvex (in an extended sense) function f using higher order Dini directional derivatives. A Variational Inequality, which is a refinement of the Stampacchia Variational Inequality, is defined. We prove that the solution set of this problem coincides with the set of global minimizers of f if and only if f is pseudoconvex. We introduce a notion of pseudomonotone Dini directional derivatives (in an extended sense). It is applied to prove that the solution sets of the Stampacchia Variational Inequality and Minty Variational Inequality coincide if and only if the function is pseudoconvex. At last, we obtain several characterizations of the solution set of a program with a pseudoconvex objective function.     

On the Bounded Variation of Operator-Valued Functions

In[1],the Kothe nuclear sequence spaces are described and in[2]the characte-rization of the semi-nuclear and the barreled locally convex spaces by the boundedvariation of functions respectively.In this paper several kinds of bounded variationof operator-valued functions are studied. Let X and Y are Banach spaces,T(t):[0,1]→L(X,Y)be a operator-valued fun-ction.We called T(t)be uniformly bounded variation,if there exist a constantM>0,such that for any partition △:0=t_0相似文献   

Heat Trace Asymptotics with Singular Weight Functions II

We study the weighted heat trace asymptotics of an operator of Laplace type with mixed boundary conditions where the weight function exhibits radial blowup. We give formulas for the first three boundary terms in the expansion in terms of geometrical data.     

Extrinsic Isoperimetric Analysis on Submanifolds with Curvatures Bounded from Below

We obtain upper bounds for the isoperimetric quotients of extrinsic balls of submanifolds in ambient spaces which have a lower bound on their radial sectional curvatures. The submanifolds are themselves only assumed to have lower bounds on the radial part of the mean curvature vector field and on the radial part of the intrinsic unit normals at the boundaries of the extrinsic spheres, respectively. In the same vein we also establish lower bounds on the mean exit time for Brownian motions in the extrinsic balls, i.e. lower bounds for the time it takes (on average) for Brownian particles to diffuse within the extrinsic ball from a given starting point before they hit the boundary of the extrinsic ball. In those cases, where we may extend our analysis to hold all the way to infinity, we apply a capacity comparison technique to obtain a sufficient condition for the submanifolds to be parabolic, i.e. a condition which will guarantee that any Brownian particle, which is free to move around in the whole submanifold, is bound to eventually revisit any given neighborhood of its starting point with probability 1. The results of this paper are in a rough sense dual to similar results obtained previously by the present authors in complementary settings where we assume that the curvatures are bounded from above.     

On Bounded Variation Functions by General MKZD Operators

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Polynomial Approximation of Functions on a Quasi-Smooth Arc with Hermitian Interpolation

We construct polynomial approximations for continuous functions f defined on a quasi-smooth (in the sense of Lavrentiev) arc L in the complex plane which simultaneously interpolate f and its derivatives at given points of L.     

An Infeasible Mizuno–Todd–Ye Type Algorithm for Convex Quadratic Programming with Polynomial Complexity

Infeasible interior point methods have been very popular and effective. In this paper, we propose a predictor–corrector infeasible interior point algorithm for convex quadratic programming, and we prove its convergence and analyze its complexity. The algorithm has the polynomial numerical complexity with O(nL)-iteration.     

Duality Theory for Optimization Problems with Interval-Valued Objective Functions

A solution concept in optimization problems with interval-valued objective functions, which is essentially similar to the concept of nondominated solution in vector optimization problems, is introduced by imposing a partial ordering on the set of all closed intervals. The interval-valued Lagrangian function and interval-valued Lagrangian dual function are also proposed to formulate the dual problem of the interval-valued optimization problem. Under this setting, weak and strong duality theorems can be obtained.     

Star Unfolding Convex Polyhedra via Quasigeodesic Loops

We extend the notion of star unfolding to be based on a quasigeodesic loop Q rather than on a point. This gives a new general method to unfold the surface of any convex polyhedron ℘ to a simple (nonoverlapping) planar polygon: cut along one shortest path from each vertex of ℘ to Q, and cut all but one segment of Q.     

Beyond Convex? Global Optimization is Feasible Only for Convex Objective Functions: A Theorem

It is known that there are feasible algorithms for minimizing convex functions, and that for general functions, global minimization is a difficult (NP-hard) problem. It is reasonable to ask whether there exists a class of functions that is larger than the class of all convex functions for which we can still solve the corresponding minimization problems feasibly. In this paper, we prove, in essence, that no such more general class exists. In other words, we prove that global optimization is always feasible only for convex objective functions.     

Locality of Quadratic Forms for Point Perturbations of Schrödinger Operators

In this paper we study point perturbations of the Schrödinger operators within the framework of Krein's theory of self-adjoint extensions. A locality criterion for quadratic forms is proved for such perturbations.