A <Emphasis Type="Italic">VU</Emphasis>-decomposition method for a second-order cone programming problem

A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given.     

Two new predictor-corrector algorithms for second-order cone programming

Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming (SOCP) are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton (AHO) directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O(rln(ɛ ₀/ɛ)) is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective.     

基于模型预测静态二阶锥规划的协同末制导

针对现有序列二阶锥规划求解协同末制导时速度较慢,难以满足实时性要求的问题,结合模型预测静态规划(MPSP)与二阶锥规划(SOCP),提出一种基于模型预测静态二阶锥规划的协同末制导算法.首先,建立考虑过载约束的飞行器协同末制导模型;然后,在MPSP算法基础上,提出终端时间自由的MPSP算法;进一步将有约束的MPSP问题转...     

Minimum principle of complementary energy of cable networks by using second-order cone programming

The minimum principle of complementary energy is established for cable networks involving only stress components as variables in geometrically nonlinear elasticity. It is rather amazing that the complementary energy always attains minimum value at the equilibrium state irrespective of the stability of cable networks, contrary to the fact that only the stationary principles have been presented for elastic trusses and continua even in the case of stable equilibrium state. In order to show the strong duality between the minimization problems of total potential energy and complementary energy, the convex formulations of these problems are investigated, which can be embedded into a primal–dual pair of second-order cone programming problems. The existence and uniqueness of solution are also investigated for the minimization problem of complementary energy.     

A method of parametric quadrature programming for the problem of osmosis-solidification in elastoplastic rock-soil medium

The process of deformation in a medium of the kind of rock-soil is a dynamic process, because there is osmosis-solidification resulting in elastic-plastic deformation. In this paper, the parametric variational method and corresponding FEM are established for dealing with this problem. The problem is reduced to solving a quadratic programming problem with restrictive conditions (constitutive state equations). The choice of element form and the specific process of implementation are discussed. Two examples are given.     

General problem of static thermoelasticity for a transversely isotropic cone

Institute of Mechanics of the Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 28, No. 12, pp. 39–46, December, 1992.     

A unified Krylov-Bogoliubov method for solving second-order non-linear systems

A unified theory is presented for obtaining the transient response of second-order non-linear systems by the Krylov-Bogoliubov method. The method is a generalization of Bogoliubov's asymptotic method and covers all three cases when the roots of the corresponding linear equation are real, complex conjugate, or pure imaginary. It is shown that by suitable substitution for the roots in the general result, that the solution corresponding to each of the three cases can be obtained. The solution for the equation governing the motion of a simple pendulum with and without damping derived from the general solution reduces to that obtained by Popov's [4] method.     

Conditions for the existence of a solution of a Noether boundary-value problem for a second-order system

We consider a weakly nonlinear boundary-value problem for a system of second-order ordinary differential equations. We find a sufficient condition for the existence of at least one solution of this problem and propose a convergent iterative algorithm for the determination of its solution. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 3, pp. 368–375, July–September, 2006.     

A boundary element method for a non-linear free surface problem

In this paper a numerical method to compute the wave resistance of a body submerged in a free stream of finite and infinite depth is presented. Non-linear effects on the free surface are taken into account by an iterative procedure; the solution is in the form of a single-layer potential. For the 2D problem, results are shown for both the cases of finite and infinite depth of the fluid domain, with special emphasis on the supercritical flow in which the consistency of the scheme is pointed out. The method is also extended to the 3D case of a spheroid submerged in deep water. All the results presented are compared with experimental data and analytical solutions available in the literature.     

A combined method for the programming of saccadic eye movements

A saccade is a quick spasmodic movement of an eye formed by the central nervous system before the beginning of the movement and is realized by the oculomotor muscles as a programmed movement. These muscles are modeled as viscoelastic contractile elements. The programmed control is defined as a time function and is considered as a sum of four components (tonic, static, kinematic, and dynamic) under the following assumption: when a muscle contracts, the corresponding antagonist muscle becomes elongated.     

A finite element method for a three-dimensional second-order closure model of turbulent diffusion in a convective boundary layer

A three-dimensional second-order closure dispersion model is used to simulate the plume behaviour of a passive contaminant in a convective boundary layer. A time-splitting finite element method together with a non-linear filtering scheme is used to solve the three-dimensional second-order closure transport equations. The model results show good agreement with laboratory data for a ground level source.     

NEWTON METHOD FOR SOLVING A CLASS OF SMOOTH CONVEX PROGRAMMING

1ConvexProgrammingandExactPenaltyFunction Weconsiderthefollowingconvexprogramming:(P)minf(x)s.t.x∈S={x∈Rn:gi(x)≤0,i=1,…,m}.SupposethatSisacompactset.ThusthereexistsalargeboundedboxX,suchthatS={x∈Rn:gi(x)≤0,i=1,…,m}intX.Assumethatf(x),gi(x),i=1,…,m     

Parametric quadratic programming method for viscoplasticity

Perzyna model in viscoplasticity has been studied by the parametric variationalprinciple,which could be transformed into solving the parametric quadratic programmingproblem.The FEM form of this problem and its implementation have also been discussed inthe paper.     

A uniform high-order method for a singular perturbation problem in conservative form

A uniform high order method is presented for the numerical solution of a singular perturbation problem in conservative form. We firest replace the original second-order problem (1.1) by two equivalent first-order problems (1.4), i.e., the solution of (1.1) is a linear combination of the solutions of (1.4). Then we derive a uniformly O(h~m+1)accurate scheme for the first-order problems (1.4), where m is an arbitrary nonnegative integer, so we can get a uniformly O(h~m+1) accurate solution of the original problem (1.1) by relation (1.3). Some illustrative numerical results are also given.