A dynamic system model for solving convex nonlinear optimization problems

This paper proposes a feedback neural network model for solving convex nonlinear programming (CNLP) problems. Under the condition that the objective function is convex and all constraint functions are strictly convex or that the objective function is strictly convex and the constraint function is convex, the proposed neural network is proved to be stable in the sense of Lyapunov and globally convergent to an exact optimal solution of the original problem. The validity and transient behavior of the neural network are demonstrated by using some examples.     

一类混合单调算子的不动点定理

运用锥理论与迭代方法,讨论了在较弱条件下一类混合单调算子的不动点的存在唯一性,所得结果是某些已有结果的本质改进和推广.     

拟树图按第二大无符号拉普拉斯特征值排序

A connected graph G=(V,E) is called a quasi-tree graph if there exists a vertex v_0∈V(G) such that G-v_0 is a tree.In this paper,we determine all quasi-tree graphs of order n with the second largest signless Laplacian eigenvalue greater than or equal to n-3.As an application,we determine all quasi-tree graphs of order n with the sum of the two largest signless Laplacian eigenvalues greater than to 2 n-5/4.     

Smoothing methods for convex inequalities and linear complementarity problems

A smooth approximationp (x, ) to the plus function max{x, 0} is obtained by integrating the sigmoid function 1/(1 + e^–x ), commonly used in neural networks. By means of this approximation, linear and convex inequalities are converted into smooth, convex unconstrained minimization problems, the solution of which approximates the solution of the original problem to a high degree of accuracy for sufficiently large. In the special case when a Slater constraint qualification is satisfied, an exact solution can be obtained for finite. Speedup over MINOS 5.4 was as high as 1142 times for linear inequalities of size 2000 × 1000, and 580 times for convex inequalities with 400 variables. Linear complementarity problems are converted into a system of smooth nonlinear equations and are solved by a quadratically convergent Newton method. For monotone LCPs with as many as 10 000 variables, the proposed approach was as much as 63 times faster than Lemke's method.This material is based on research supported by Air Force Office of Scientific Research Grant F49620-94-1-0036 and National Science Foundation Grants CCR-9101801 and CCR-9322479.     

ON EQUILIBRIUM PRICING AS CONVEX OPTIMIZATION

We study competitive economy equilibrium computation. We show that, for the first time, the equilibrium sets of the following two markets： 1. A mixed Fisher and Arrow- Debreu market with homogeneous and log-concave utility functions; 2. The Fisher and Arrow-Debreu markets with several classes of concave non-homogeneous utility functions; are convex or log-convex. Furthermore, an equilibrium can be computed as convex opti- mization by an interior-point algorithm in polynomial time.     

The potential energy surface and chaos in 2D Hamiltonian systems

We provide a new insight into the relationship between the geometric property of the potential energy surface and chaotic behavior of 2D Hamiltonian dynamical systems, and give an indicator of chaos based on the geometric property of the potential energy surface by defining Mean Convex Index (MCI). We also discuss a model of unstable Hamiltonian in detail, and show our results in good agreement with HBLSL's (Horwitz, Ben Zion, Lewkowicz, Schiffer and Levitan) new Riemannian geometric criterion.     

Inverse optimization for linearly constrained convex separable programming problems

In this paper, we study inverse optimization for linearly constrained convex separable programming problems that have wide applications in industrial and managerial areas. For a given feasible point of a convex separable program, the inverse optimization is to determine whether the feasible point can be made optimal by adjusting the parameter values in the problem, and when the answer is positive, find the parameter values that have the smallest adjustments. A sufficient and necessary condition is given for a feasible point to be able to become optimal by adjusting parameter values. Inverse optimization formulations are presented with ℓ₁ and ℓ₂ norms. These inverse optimization problems are either linear programming when ℓ₁ norm is used in the formulation, or convex quadratic separable programming when ℓ₂ norm is used.     

Enveloppes convexes des processus gaussiens

Let X={X(t), t[0,1]} be a process on [0,1] and V_X=Conv{(t,x)t[0,1], x=X(t)} be the convex hull of its path.The structure of the set ext(V_X) of extreme points of V_X is studied. For a Gaussian process X with stationary increments it is proved that:

• The set ext(V_X) is negligible if X is non-differentiable.

• If X is absolutely continuous process and its derivative X′ is continuous but non-differentiable, then ext(V_X) is also negligible and moreover it is a Cantor set.

It is proved also that these properties are stable under the transformations of the type Y(t)=f(X(t)), if f is a sufficiently smooth function.     

Antiferromagnetic Ordering in TmCu2

Intermetallic compound TmCu₂ crystalizes in the orthorhombic structure, orders antiferromagnetically (AF) and exhibits four different AF phases below T _N = 6.5 K. In all these phases the Tm magnetic moment is parallel to the b-axis. The ground-state AF1 (T < 3.4 K) corresponds to the squared-up AF structure with propagation vector ₀₁ = (5/8, 0, 0) and magnetic unit cell 8a × b × c. Narrow phases AF2 and AF3 (3.3 K < T < 3.7 K and 3.6 K < T < 4.6 K) are 'spin-slip'-derivatives from the AF1 structure, yielding propagation vectors ₀₂ = (0.633, 0, 0.02) and ₀₃ = (0.618, 0, 0), respectively. The phase AF4 (4.4 K < T < T _N) is then incommensurate transversal spin-wave with the propagation ₀₄ = (0.64, 0, 0). The co-existence of AF phases indicates the first-order transitions between them.     

Tetrachloroferrate (III) Salts of BDH-TTP [2,5-Bis(1,3-dithiolan-2-ylidene)-1,3,4,6-tetrathiapentalene] and BDA-TTP [2,5-Bis(1,3-dithian-2-ylidene)-1,3,4,6-tetrathiapentalene]: Crystal Structures and Physical Properties

Three FeCl₄ salts based on non-tetrathiafulvalene (TTF) donors, 2,5-bis(1,3-dithiolan-2-ylidene)-1,3,4,6-tetrathiapentalene (BDH-TTP) and 2,5-bis(1,3-dithian-2-ylidene)-1,3,4,6-tetrathiapentalene (BDA-TTP), have been prepared and characterized as κ-(BDH-TTP)₂FeCl₄, β-(BDA-TTP)₂FeCl₄, and (BDA-TTP)₃FeCl₄ · PhCl. The κ-(BDH-TTP)₂FeCl₄ salt, with a room-temperature conductivity (σ_rt) of 39 S cm⁻¹, is metallic down to 1.5 K, and its magnetic susceptibility obeys the Curie-Weiss law with a Curie constant (C) of 4.25 emu K mol⁻¹ and a Weiss constant (θ) of 0.041 K. β-(BDA-TTP)₂FeCl₄ exhibits metallic behavior (σ_rt=9.4 S cm⁻¹) with a sharp metal-to-insulator (MI) transition (T_MI=113 K) and antiferromagnetic ordering with the Néel temperature of near 8.5 K, whereas the solvated (BDA-TTP)₃FeCl₄ · PhCl salt is a semiconductor with a thermal activation energy of 0.11 eV (σ_rt=2.0× 10⁻² S cm⁻¹) and exhibits Curie-Weiss behavior (C=4.42 emu K mol⁻¹, θ=−0.35 K).