Semiconcavity results for constrained optimal control problems in a half-space

In this paper we give semiconcavity results for the value function of some constrained optimal control problems with infinite horizon in a half-space. In particular, we assume that the control space is the l¹-ball or the l^∞-ball in Rn.     

线性均衡约束最优化的一个广义投影强次可行方向法

本文讨论带线性均衡约束最优化问题,首先利用摄动技术和一个互补函数将问题等价转化为一般约束最优化问题,然后结合广义投影技术和强次可行方向法思想,建立了问题的一个新算法.算法在迭代过程中保证搜索方向不为零,从而使得每次迭代只需计算一次广义投影.在适当的条件下,证明了算法的全局收敛性,并对算法进行了初步的数值试验.     

遗传算法求解约束非线性规划及Matlab实现

对于约束非线性规划问题,传统的方法:可行方向法、惩罚函数法计算烦琐且精度不高.用新兴的遗传算法来解决约束非线性规划,核心是惩罚函数的构造.以前的惩罚函数遗传算法有的精度较低,有的过于复杂.本文在两个定义的基础上构造了新的惩罚函数,并在新的惩罚函数的基础上,提出了一种解决约束非线性最优化问题的方法.通过两个例子应用Matlab说明了这个算法的可行性.     

Block-Coordinate Gradient Descent Method for?Linearly Constrained Nonsmooth Separable Optimization

We consider the problem of minimizing the weighted sum of a smooth function f and a convex function P of n real variables subject to m linear equality constraints. We propose a block-coordinate gradient descent method for solving this problem, with the coordinate block chosen by a Gauss-Southwell-q rule based on sufficient predicted descent. We establish global convergence to first-order stationarity for this method and, under a local error bound assumption, linear rate of convergence. If f is convex with Lipschitz continuous gradient, then the method terminates in O(n ²/ε) iterations with an ε-optimal solution. If P is separable, then the Gauss-Southwell-q rule is implementable in O(n) operations when m=1 and in O(n ²) operations when m>1. In the special case of support vector machines training, for which f is convex quadratic, P is separable, and m=1, this complexity bound is comparable to the best known bound for decomposition methods. If f is convex, then, by gradually reducing the weight on P to zero, the method can be adapted to solve the bilevel problem of minimizing P over the set of minima of f+δ _X , where X denotes the closure of the feasible set. This has application in the least 1-norm solution of maximum-likelihood estimation. This research was supported by the National Science Foundation, Grant No. DMS-0511283.     

A Class of Quadratic Programs with Linear Complementarity Constraints

We consider a class of quadratic programs with linear complementarity constraints (QPLCC) which belong to mathematical programs with equilibrium constraints (MPEC). We investigate various stationary conditions and present new and strong necessary and sufficient conditions for global and local optimality. Furthermore, we propose a Newton-like method to find an M-stationary point in finite steps without MEPC linear independence constraint qualification. The research of this author is partially supported by NSERC, and Research Grand Council of Hong Kong.     

A maximum principle for smooth optimal impulsive control problems with multipoint state constraints

A nonlinear optimal impulsive control problem with trajectories of bounded variation subject to intermediate state constraints at a finite number on nonfixed instants of time is considered. Features of this problem are discussed from the viewpoint of the extension of the classical optimal control problem with the corresponding state constraints. A necessary optimality condition is formulated in the form of a smooth maximum principle; thorough comments are given, a short proof is presented, and examples are discussed.     

A virtual control concept for state constrained optimal control problems

A linear elliptic control problem with pointwise state constraints is considered. These constraints are given in the domain. In contrast to this, the control acts only at the boundary. We propose a general concept using virtual control in this paper. The virtual control is introduced in objective, state equation, and constraints. Moreover, additional control constraints for the virtual control are investigated. An error estimate for the regularization error is derived as main result of the paper. The theory is illustrated by numerical tests.     

Lipschitz stability for elliptic optimal control problems with mixed control-state constraints

A family of linear-quadratic optimal control problems with pointwise mixed state-control constraints governed by linear elliptic partial differential equations is considered. All data depend on a vector parameter of perturbations. Lipschitz stability with respect to perturbations of the optimal control, the state and adjoint variables, and the Lagrange multipliers is established.     

Adaptive limited memory bundle method for bound constrained large-scale nonsmooth optimization

Typically, practical optimization problems involve nonsmooth functions of hundreds or thousands of variables. As a rule, the variables in such problems are restricted to certain meaningful intervals. In this article, we propose an efficient adaptive limited memory bundle method for large-scale nonsmooth, possibly nonconvex, bound constrained optimization. The method combines the nonsmooth variable metric bundle method and the smooth limited memory variable metric method, while the constraint handling is based on the projected gradient method and the dual subspace minimization. The preliminary numerical experiments to be presented confirm the usability of the method.     

Existence and generic stability of solutions for multiclass multicriteria traffic equilibrium problems with capacity constraints of arcs

ABSTRACT

In this paper, we introduce the multiclass multicriteria traffic equilibrium problem with capacity constraints of arcs and its equilibrium principle. Using Fan–Browder's fixed points theorem and Fort's lemma to prove the existence and generic stability results of multiclass multicriteria traffic equilibrium flows with capacity constraints of arcs.