Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

<p style='text-indent:20px;'>In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law of elastic-viscoplastic materials has an implicit expression of the stress field, the weak form of the model is an evolutionary hemivariational inequality coupled with an integral equation. By providing some equivalent weak formulations, we prove the continuous dependence of the solution on external forces and initial conditions in the weak topologies. Finally, the existence of optimal solutions to a boundary optimal control problem is established.</p>

Optimal Control of a Nonlinear PDE Governed by Fractional Laplacian

We consider an optimal control problem containing a control system described by a partial nonlinear differential equation with the fractional Dirichlet–Laplacian, associated to an integral cost. We investigate the existence of optimal solutions for such a problem. In our study we use Filippov’s approach combined with a lower closure theorem for orientor fields.

Optimal control of static contact in finite strain elasticity

We consider the optimal control of elastic contact problems in the regime of finite deformations. We derive a result on existence of optimal solutions and propose a regularization of the contact constraints by a penalty formulation. Subsequential convergence of sequences of solutions of the regularized problem to original solutions is studied. Based on these results, a numerical path-following scheme is constructed and its performance is tested.

Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables

The numerical method for solving the fuzzy linear programming problems with fuzzydecision variables is proposed in this paper. The difficulty for solving this kind of problem is thatthe decision variables are assumed to be nonnegative fuzzy numbers instead of nonnegative realnumbers. In other words, the decision variables are assumed to be membership functions. One of thepurposes of this paper is to derive the analytic formula of error estimation regarding the approximateoptimal solution. On the other hand, the existence of optimal solutions is also studied in this paper.Finally we present two numerical examples to demonstrate the usefulness of the numerical method.

Stationary Gas Networks with Compressor Control and Random Loads: Optimization with Probabilistic Constraints

We introduce a stationary model for gas flow based on simplified isothermal Euler equations in a non-cycled pipeline network. Especially the problem of the feasibility of a random load vector is analyzed. Feasibility in this context means the existence of a flow vector meeting these loads, which satisfies the physical conservation laws with box constraints for the pressure. An important aspect of the model is the support of compressor stations, which counteract the pressure loss caused by friction in the pipes. The network is assumed to have only one influx node; all other nodes are efflux nodes. With these assumptions the set of feasible loads can be characterized analytically. In addition we show the existence of optimal solutions for some optimization problems with probabilistic constraints. A numerical example based on real data completes this paper.

Boundary Control Problem for Heat Convection Equations with Slip Boundary Condition

We analyze an optimal boundary control problem for heat convection equations in a three-dimensional domain, with mixed boundary conditions. We prove the existence of optimal solutions, by considering boundary controls for the velocity vector and the temperature. The analyzed optimal control problem includes the minimization of a Lebesgue norm between the velocity and some desired field, as well as the temperature and some desired temperature. By using the Lagrange multipliers theorem we derive an optimality system. We also give a second-order sufficient condition.