A discrete optimality system for an optimal harvesting problem

In this paper, we obtain the discrete optimality system of an optimal harvesting problem. While maximizing a combination of the total expected utility of the consumption and of the terminal size of a population, as a dynamic constraint, we assume that the density of the population is modeled by a stochastic quasi-linear heat equation. Finite-difference and symplectic partitioned Runge–Kutta (SPRK) schemes are used for space and time discretizations, respectively. It is the first time that a SPRK scheme is employed for the optimal control of stochastic partial differential equations. Monte-Carlo simulation is applied to handle expectation appearing in the cost functional. We present our results together with a numerical example. The paper ends with a conclusion and an outlook to future studies, on further research questions and applications.     

A necessary condition of optimality for uncertain optimal control problem

This paper is concerned with optimal control problem whose state equation is an uncertain differential equation. A necessary condition of optimality for uncertain optimal control problem is presented by using classical variational method. Meanwhile, an existence theorem of solution to backward uncertain differential equation is proved.     

An adaptive parameter approach for an approximate solution of optimal control problems

In this paper, we consider a class of nonlinear optimal control problems (Bolza-problems) with constraints of the control vector, initial and boundary conditions of the state vectors. The time interval is fixed. Our approach to parametrize both the state functions and the control functions is described by general piecewise polynomials with unknown coefficients (parameters), where a fixed partition of the time interval is used. Here each of these functions in a suitable way individually will be approximated by such polynomials. The optimal control problem thus is reduced to a mathematical programming problem for these parameters. The existence of an optimal solution is assumed. Convergence properties of this method are not considered in this paper.     

Sensitivity of parameter estimates to observations,system identification,and optimal inputs

The sensitivity of parameter estimates to observation noise or disturbances affects the accuracy of the parameter estimates in system identification. The (parameter estimate)/observation sensitivity is derived for a scalar nonlinear differential system. In the design of optimal inputs, the sensitivity of the state variable to the unknown parameter is maximized. It is shown that the (parameter estimate)/observation sensitivity tends to be lowered for optimal inputs. A numerical example is given.     

Necessary conditions for optimality in the identification of elliptic systems with parameter constraints

We consider the problems of dientifying the parametersa _ij (x), b _i (x), c(x) in a 2nd order, linear, uniformly elliptic equation, $$\begin{gathered} - \partial _i (a_{ij} (x)\partial _j u) + b_i (x)\partial _i u + c(x)u = f(x),in\Omega , \hfill \\ \partial _v u|_{\partial \Omega } = \phi (s),s \in \partial \Omega , \hfill \\ \end{gathered} $$ on the basis of measurement data $$u(s) = z(s),s \in B \subset \partial \Omega ,$$ with an equality constraint and inequality constraints on the parameters. The cost functionals are one-sided Gâteaux differentiable with respect to the state variables and the parameters. Using the Duboviskii-Milyutin lemma, we get maximum principles for the identification problems, which are necessary conditions for the existence of optimal parameters.     

Existence of optimal solution for exponential model by least squares

In this paper we prove the existence theorem for the best least squares approximation of the optimal parameters for the exponential model function. We give sufficient conditions which guarantee the existence of such optimal parameters. Using these results and methods, we are able to localize a sufficiently narrow area where one can choose a good initial approximation.     

Numerical solution of optimal control problems for loaded lumped parameter systems

An optimal control problem for the system of linear (with respect to phase variables) loaded ordinary differential equations with initial (local) and nonseparated multipoint (nonlocal) conditions is investigated. Necessary optimality conditions are obtained, numerical schemes of their solution are proposed, and results of numerical experiments are presented.     

Existence and optimality of w-non-adjacent forms with an algebraic integer base

We consider digit expansions in lattices with endomorphisms acting as base. We focus on the w-non-adjacent form (w-NAF), where each block of w consecutive digits contains at most one non-zero digit. We prove that for sufficiently large w and an expanding endomorphism, there is a suitable digit set such that each lattice element has an expansion as a w-NAF. If the eigenvalues of the endomorphism are large enough and w is sufficiently large, then the w-NAF is shown to minimise the weight among all possible expansions of the same lattice element using the same digit system.     

Existence results for a nonlinear system with a parameter

In this paper, the monotone operator principle, the critical point theory and the morse theory are employed to discuss the system of nonlinear equations of the form Au=λf(u), some existence results are obtained.     

Existence of solutions for a nonlinear system with a parameter

In this paper, the existence of solutions for a system of nonlinear equations is considered. n² nonzero real solutions are obtained by using the critical point theory. Additionally, the Dirichlet boundary value problems of even order difference equations and partial difference equations are investigated.     

Existence and multiple solutions for a nonlinear system with a parameter

In this paper, the critical point theory and the Morse theory are employed to discuss the system of nonlinear equations of the form Au=λf(u)$Au=\lambda f\left(u\right)$, where the matrix A$A$ is not necessarily positive definite. Some existence and multiple solutions are obtained.     

No-gap optimality conditions for an optimal control problem with pointwise control-state constraints

An optimal control problem with pointwise mixed constraints of the instationary three-dimensional Navier–Stokes–Voigt equations is considered. We derive second-order optimality conditions and show that there is no gap between second-order necessary optimality conditions and second-order sufficient optimality conditions. In addition, the second-order sufficient optimality conditions for the problem where the objective functional does not contain a Tikhonov regularization term are also discussed.     

Constructing an asymptotic solution of optimal observation problem for a quasilinear differential-algebraic system

The known results on the problem of optimal observation for ordinary quasilinear systems are generalized to differential-algebraic systems.     

集值优化问题在Henig真有效解意义下的导数型最优性条件

给出实的赋范空间中集值映射的Henig真有效解集的一些性质,并利用集值映射的相依上图导数和集值映射的次微分给出了集值优化问题Henig真有效解的最优性条件的充要条件.     

Existence of non-zero solutions for a nonlinear system with a parameter

In this paper, the existence of solutions for a system of nonlinear equations is considered. 2ⁿ$2^n$ non-zero real solutions are obtained by using the critical point theory. Some known results are improved.     

一类海冰-海水耦合热力学系统参数辨识问题的最优性

针对一维的海冰-海水耦合热力学系统,以该系统中的物理参数为辨识量,以温度偏差为目标函数,建立了一个参数辨识模型,并证明了该问题最优解的存在性,从而为这类海冰-海水耦合热力学系统参数辨识问题的数值计算提供数学理论依据.     

Exact solution for an optimal impermeable parachute problem

In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle—the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.