A locally polynomial method for solving a system of linear inequalities

The paper proposes a method for solving systems of linear inequalities. This method determines in a finite number of iterations whether the given system of linear ineqalities has a solution. If it does, the solution for the given system of linear inequalities is provided. The computational complexity of the proposed method is locally polynomial

Automatic Differentiation And Spectral Projected Gradient Methods For Optimal Control Problems

this paper is to show the application of these canonical formulas to optimal control processes being integrated by the Runge-Kutta family of numerical methods. There are many papers concerning numerical comparisions between automatic differentiation, finite differences and symbolic differentiation. See, for example, [1, 2, 6, 7, 21] among others. Another objective is to test the behavior of the spectral projected gradient methods introduced in [5]. These methods combine the classical projected gradient with two recently developed ingredients in optimization: (i) the nonmonotone line search schemes of Grippo, Lampariello and Lucidi ([24]), and (ii) the spectral steplength (introduced by Barzilai and Borwein ([3]) and analyzed by Raydan ([30, 31])). This choice of the steplength requires little computational work and greatly speeds up the convergence of gradient methods. The numerical experiments presented in [5], showing the high performance of these fast and easily implementable methods, motivate us to combine the spectral projected gradient methods with automatic differentiation. Both tools are used in this work for the development of codes for numerical solution of optimal control problems. In Section 2 of this paper, we apply the canonical formulas to the discrete version of the optimal control problem. In Section 3, we give a concise survey about spectral projected gradient algorithms. Section 4 presents some numerical experiments. Some final remarks are presented in Section 5. 2 CANONICAL FORMULAS The basic optimal control problem can be described as follows: Let a process governed by a system of ordinary differential equations be dx(t) dt = f(x(t); u(t); ); T 0 t T f ; (1) where x : [T 0 ; T f ] ! IR nx , u : [T 0 ; T f ] ! U ` IR nu , U compact, and 2 V ..

11th International Conference on Optimization and Applications

This book constitutes the refereed proceedings of the 11th International Conference on Optimization and Applications, OPTIMA 2020, held in Moscow, Russia, in September-October 2020.* The 21 full and 2 short papers presented were carefully reviewed and selected from 60 submissions. The papers cover such topics as mathematical programming, combinatorial and discrete optimization, optimal control, optimization in economics, finance, and social sciences, global optimization, and applications. * The conference was held virtually due to the COVID-19 pandemic

Cluster Generation Under Pulsed Laser Ablation Of Compound Semiconductors

International audienceA comparative experimental study of pulsed laser ablation in vacuum of two binary semiconductors, zinc oxide and indium phosphide, has been performed using IR-and visible laser pulses with particular attention to cluster generation. Neutral and cationic Zn_n O_m and In_n P_m particles of various stoichiometry have been produced and investigated by time-of-flight mass spectrometry. At ZnO ablation, large cationic (n>9) and all neutral clusters are mainly stoichiometric in the ablation plume. In contrast, indium phosphide clusters are strongly indium-rich with In_4 P being a magic cluster. Analysis of the plume composition upon laser exposure has revealed congruent vaporization of ZnO and a disproportionate loss of phosphorus by the irradiated InP surface. Plume expansion conditions under ZnO ablation are shown to be favourable for stoichiometric cluster formation. A delayed vaporization of phosphorus under InP ablation has been observed that results in generation of off-stoichiometric clusters