Optimal Solutions of Linear Periodic Control Systems with Convex Integrands

In this work we study the existence and asymptotic behavior of overtaking optimal trajectories for linear control systems with convex integrands. We extend the results obtained by Artstein and Leizarowitz for tracking periodic problems with quadratic integrands [2] and establish the existence and uniqueness of optimal trajectories on an infinite horizon. The asymptotic dynamics of finite time optimizers is examined. Accepted 31 January 1996     

Vector Minimization of Upper Robust Mappings

1.IntroductionLetXbeatopologicalspaceandf=(f',f',...):X-Reamapping.Inthispaper,weconsiderthevectoroptimizationproblemswithrespecttothepartialorderinginducedb}'thenonnegativeorthantoftheproductspaceRe.Apointx6Xissaidtobeaegcientsolutionornondominatedsoluti…     

关于宏观经济的凸二次规划模型

本文运用凸二次规划理论，通过引入价格变量建立观经济的凸二次规划模型．并指出在社会主义市场经济中企业、产业、国家可以同时达到最优．     

Lagrange multipliers and generalized differentiable functions in vector extremum problems

In this paper, we establish a necessary optimality condition for a nondifferentiable vector extremum problem which involves a generalized vector-valued Lagrangian function. Such a condition is stated for a wide class of functions, which embraces the differentiable ones and a subclass of locally Lipschitzian functions. The condition embodies the classic theorem of F. John in multiobjective optimization.This research was partially supported by the Ministry of Public Education, Rome, Italy.     

Dynamic Programming, the Fermat Principle, and the Eikonal Equation Revisited

We derive the eikonal equation using the technique of dynamic programming. The formalism of dynamic programming is based on the procedure defining the minimum pathway, and an immediate application of the Fermat principle leads to the well-known eikonal equation of classical geometrical optics.     

A numerical method for reflected diffusions: Control of the reflection directions and applications

We are concerned with a numerical method for the optimal control of the reflection directions of a reflected diffusion process, and with either a discounted or an ergodic cost criterion. The Markov chain approximation method is adapted to this nonclassical problem and convergence of the method is proved. The problem originally arose in the important application of rerouting in large trunk-line communications systems. A reasonable heavy-traffic approximation leads to the described model. The numerical method has been applied with success, but no proofs of convergence were given previously. Nonboundary controls can be easily added.This work was partially supported by Grants (AFOSR) F49620-92-J-008-1DEF, AFOSR-91-0375, and DAAH04-93-6-0070.     

Convex composite minimization withC 1,1 functions

In this paper, we present second-order optimality conditions for convex composite minimization problems in which the objective function is a composition of a finite-valued or a nonfinite-valued lower semicontinuous convex function and aC ^1,1 function. The results provide optimality conditions for composite problems under reduced differentiability requirements.This paper is a revised version of the Departmental Preliminary Report AM92/32, School of Mathematics, University of New South Wales, Kensington, NSW, Australia.Research of this author was supported in part by an Australian Research Council Grant.     

On the reciprocal vector optimization problems

A necessary and sufficient condition is established for an optimal solution of a primal vector optimization problem to be an optimal solution of its reciprocal. Such a condition is developed and analyzed in the Pareto case, the strong case, and the lexicographic case. We detail these results for ordinary (i.e., scalar) optimization problems.     

On the optimal shape of a hydrofoil

On the basis of the results on domain shape optimization for elliptic systems developed in Ref. 1, the problem of the optimal shape of a hydrofoil, moving slowly in a viscous incompressible fluid, is formulated and studied. The otpimization problem consists in finding the shape of the hydrofoil having minimal drag, while satisfying certain constraints on the volume and hydrodynamic lift.     

Solution of linear complementarity problems using minimization with simple bounds

We define a minimization problem with simple bounds associated to the horizontal linear complementarity problem (HLCP). When the HLCP is solvable, its solutions are the global minimizers of the associated problem. When the HLCP is feasible, we are able to prove a number of properties of the stationary points of the associated problem. In many cases, the stationary points are solutions of the HLCP. The theoretical results allow us to conjecture that local methods for box constrained optimization applied to the associated problem are efficient tools for solving linear complementarity problems. Numerical experiments seem to confirm this conjecture.This work was supported by FAPESP (grants 90-3724-6 and 91-2441-3), CNPq and FAEP (UNICAMP).