In order to decrease the fluid drag on an underwater robot manipulator, an optimal trajectory method based on the variational method is presented. By introducing the adjoint variables, which are Lagrange multipliers, we formulate a Lagrange function under certain constraints related to the target angle, target angular velocity, and dynamic equation of the robot manipulator. The state equation (...

The approximate solution of optimization and control problems for systems governed by the Stokes equations is considered. Modern computational techniques for such problems are predominantly based on the application of the Lagrange multiplier rule, while penalty formulations, even though widely used in other settings, have not enjoyed the same level of popularity for this class of problems. A di...

The paper describes two iterative algorithms for solving general systems of M simultaneous linear algebraic equations (SLAE) with real matrices of coefficients. The system can be determined, underdetermined, and overdetermined. Linearly dependent equations are also allowed. Both algorithms use the method of Lagrange multipliers to transform the original SLAE into a positively determined functio...

‎In this paper, using the idea of convexificators, we study boundedness and nonemptiness of Lagrange multipliers satisfying the first order necessary conditions. We consider a class of nons- mooth fractional programming problems with equality, inequality constraints and an arbitrary set constraint. Within this context, define generalized Mangasarian-Fromovitz constraint qualification and sh...

Lagrange multipliers used to be viewed as auxiliary variables introduced in a problem of constrained minimization in order to write first-order optimality conditions formally as a system of equations. Modern applications, with their emphasis on numerical methods and more complicated side conditions than equations, have demanded deeper understanding of the concept and how it fits into a larger t...

Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring question in regularization approaches is the selection of regularization parameters, and its effect on the solution and on the optimal value of the optimization problem. The sensitivity of the value function to the regularization parameter can be linked directly to the Lagrange multipliers...

In this paper we deal with the perceptually motivated signal subspace methods for speech enhancement. We focus on extended spectral-domain-constrained (SDC) estimator. It is obtained using Lagrange multipliers method. We present an algorithm for a precise computation of the Lagrange multipliers, allowing for a direct shaping the residual noise power spectrum. In addition the SDC estimator is pr...