The Linear Nonconvex Generalized Gradient and Lagrange Multipliers

Lagrange Multipliers for Nonconvex Generalized Gradients with Equality, Inequality and Set Constraints

A Lagrange multiplier rule for nite dimensional Lipschitz problems is proven that uses a nonconvex generalized gradient. This result uses either both the linear generalized gradient and the generalized gradient of Mordukhovich or the linear generalized gradient and a qualiication condition involving the pseudo-Lipschitz behavior of the feasible set under perturbations. The optimization problem ...

A Nonoverlapping Domain Decomposition Method for Incompressible Stokes Equations with Continuous Pressures

A non-overlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the proposed algorithm, Lagrange multipliers are used to enforce continuity of the velocity component across the subdomain boundary. The continuity of the pressur...

The Linear Nonconvex Generalized Gradient

A new nonconvex generalized gradient is deened and some of its calculus is developed. This generalized gradient is smaller than that of Mordukhovich but still has a good calculus. This calculus includes a rule for the linear generalized gradient of positive multiples of functions, a sum rule and a chain rule.

An effective optimization algorithm for locally nonconvex Lipschitz functions based on mollifier subgradients

Two Iterative Algorithms for Solving Systems of Simultaneous Linear Algebraic Equations with Real Matrices of Coefficients

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...