A SUPERLINEARLY CONVERGENT SPLITTING FEASIBLE SEQUENTIAL QUADRATIC OPTIMIZATION METHOD FOR TWO-BLOCK LARGE-SCALE SMOOTH OPTIMIZATION

This paper discusses the two-block large-scale nonconvex optimization problem with general linear constraints.Based on the ideas of splitting and sequential quadratic optimization(SQO),a new feasible descent method for the discussed problem is proposed.First,we consider the problem of quadratic optimal(QO)approximation associated with the current feasible iteration point,and we split the QO into two small-scale QOs which can be solved in parallel.Second,a feasible descent direction for the problem is obtained and a new SQO-type method is proposed,namely,splitting feasible SQO(SF-SQO)method.Moreover,under suitable conditions,we analyse the global convergence,strong convergence and rate of superlinear convergence of the SF-SQO method.Finally,preliminary numerical experiments regarding the economic dispatch of a power system are carried out,and these show that the SF-SQO method is promising.

MULTIPLE POSITIVE SOLUTIONS TO SINGULAR BOUNDARY VALUE PROBLEMS FOR SUPERLINEAR SECOND ORDER ODES

This paper deals with the existence of positive solutions to the singular boundary value problemwhere q(t) may be singular at t = 0 and t = 1, f(t,y) may be superlinear at y =∞ and singular, at y = 0.

A QP-FREE AND SUPERLINEARLY CONVERGENT ALGORITHM FOR INEQUALITY CONSTRAINED OPTIMIZATIONS

In this paper, a new mixed quasi-Newton method for inequality constrained optimization problems is proposed. The feature of the method is that only the systems of linear equations are solved in each iteration, other than the quadratic programming, which decrease the amount of computations and is also efficient for large scale problem. Under some mild assumptions without the strict complementary condition., the method is globally and superlinearly convergent.

A SUPERLINEARLY CONVERGENT TRUST REGION ALGORITHM FOR LC^1 CONSTRAINED OPTIMIZATION PROBLEMS

In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subprobiem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.

Existence of Positive Solution for Superlinear Semipositone Singular Second-order m-point Boundary Value Problem

由使用固定的点定理，积极答案的存在为 superlinear semipositone 被认为单个m点边界价值问题--(n)(x)= f ( x ，(x))+ g (x)， 0 < x < 1 ，( 0 ) =0 ，( 1 )= m-2i=1 ai (i)，吗在哪儿(L)(x)=( p (x)“(x))”+ q (x)(x)和 i ( 0 ， 1 )与 0 < 1 < 2 << m-2 < 1 ， ai R+， f C [( 0,1 )???嘠???畭瑬杩楲???????牥業整？？

EXISTENCE OF SOLUTIONS FOR NON-PERIODIC SUPERLINEAR SCHRDINGER EQUATIONS WITHOUT (AR) CONDITION

The existence of solutions is obtained for a class of the non-periodic SchrSdinger equation -△u ＋ V（x）u = f（x,u）, x E RN, by the generalized mountain pass theorem, where V is large at infinity and f is superlinear as ｜u｜→ ∞.

MULTIPLE POSITIVE SOLUTIONS FOR FIRST ORDER IMPULSIVE SUPERLINEAR INTEGRO-DIFFERENTIAL EQUATIONS ON THE HALF LINE

In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.

A GLOBALLY AND SUPERLINEARLY CONVERGENT TRUST REGION METHOD FOR LC^1 OPTIMIZATION PROBLEMS

A new trust region algorithm for solving convex LC 1 optimization problem is presented.It is proved that the algorithm is globally convergent and the rate of convergence is superlinear under some reasonable assumptions.

An Oscillation Criterion for Second Order Superlinear Differential Equations

A new criterion is established for the oscillation of second order superlinear ordinary differential equations of the formx″(t) + p(t)x′(t) + q(t)｜x(t)｜αsgnx(t) = 0, t ≥ t0,where α>1,p and q are continuous functions on[t0,∞). This criterion extends and unifies some of the results obtained in [1]- [5].

Resonant-Superlinear Nonhomogeneous Dirichlet Problems

We consider a Dirichlet nonlinear equation driven by the(p,2)-Laplacian and with a reaction having the competing effects of a parametric asymmetric superlinear term and a resonant perturbation.We show that for all small values of the parameter the problem has at least five nontrivial smooth solutions all with sign information.

POSITIVE SOLUTIONS OF SINGULAR SUPERLINEAR SECOND ORDER BOUNDARY VALUE PROBLEMS

This paper is consider the boundary value problems of singular superlinear second order differential equations. A sufficient condition for the existence of positive solutions to this problem has been obtained by using the fixed point theorems on cones.

Existence of periodic and subharmonic solutions for second-order superlinear difference equations

By critical point theory, a new approach is provided to study the existence and multiplicity results of periodic and subharmonic solutions for difference equations. For secord-order difference equations △2xn-1 + f(n,xn) = 0,some new results are obtained for the above problems when f(t, z) has superlinear growth at zero and at infinity in z.

The Superlinear Convergence Analysis of a Nonmonotone BFGS Algorithm on Convex Objective Functions

We prove the superlinear convergence of a nonmonotone BFGS algorithm on convex objective functions under suitable conditions.

Superlinear/Quadratic One-step Smoothing Newton Method for P_0-NCP

We propose a one–step smoothing Newton method for solving the non-linearcomplementarity problem with P 0–function (P_0–NCP) based on the smoothing symmetric perturbedFisher function (for short, denoted as the SSPF–function). The proposed algorithm has to solve onlyone linear system of equations and performs only one line search per iteration. Without requiringany strict complementarity assumption at the P_0–NCP solution, we show that the proposed algorithmconverges globally and superlinearly under mild conditions. Furthermore, the algorithm has localquadratic convergence under suitable conditions. The main feature of our global convergence resultsis that we do not assume a priori the existence of an accumulation point. Compared to the previousliteratures, our algorithm has stronger convergence results under weaker conditions.

BOUNDEDNESS FOR SOLUTIONS OF SUPERLINEAR DUFFING EQUATIONS VIA THE TWIST THEOREM

A class of functions {g(x)} will be provided, such that the differential equation d^2x/dt^2+ g(x) = p(t) possesses an infinitely many number of invariant tori in the orbit space(t, x,dx/dt)∈S^1×R^2. Moreover, each solution of the equation is bounded. The proof is basedon the twist theorem.

Homoclinic Solutions in Periodic Nonlinear Difference Equations with Superlinear Nonlinearity

In this paper, we consider the existence of homoclinic solutions in periodic nonlinear difference equations with superlinear nonlinearity. The classical Ambrosetti–Rabinowitz superlinear condition is improved by a general superlinear one. The proof is based on the critical point theory in combination with periodic approximations of solutions.

A New Superlinearly Convergent SQP Algorithm for Nonlinear Minimax Problems

In this paper, the nonlinear minimax problems are discussed. By means of the Sequential Quadratic Programming （SQP）, a new descent algorithm for solving the problems is presented. At each iteration of the proposed algorithm, a main search direction is obtained by solving a Quadratic Programming （QP） which always has a solution. In order to avoid the Maratos effect, a correction direction is obtained by updating the main direction with a simple explicit formula. Under mild conditions without the strict complementarity, the global and superlinear convergence of the algorithm can be obtained. Finally, some numerical experiments are reported.

A Superlinearly Convergent Combined PhaseⅠ-PhaseⅡ Subfeasible Method

This paper presents a new algorithm for optimization problems with nonlinear inequality constricts. At each iteration, the algorithm generates the search direction by solving only one quadratic programming (QP), and then making a simple correction for the solution of the QP, moreover this new algorithm needn’t to do searching. The other advantage is that it may not only choose any point in En as a starting point, but also escape from the complex penalty function and diameter. moreover the iteration point will be a feasible descent sequence whenever some iteration point gets into the feasible region. So we call it subfeasible method.Under mild assumptions,the new algorithm is shown to possess global and two step superlinear convergence.

A Strong Subfeasible Directions Algorithm with Superlinear Convergence

This paper presents a strong subfeasible directions algorithm possessing superlinear convergence for inequality constrained optimization. The starting point of this algorithm may be arbitary and its feasibility is monotonically increasing. The search directions only depend on solving one quadratic proraming and its simple correction, its line search is simple straight search and does not depend on any penalty function. Under suit assumptions, the algorithm is proved to possess global and superlinear convergence.