In this paper, using theorems on the continuous dependence of solution differential inclusions perturbation, we obtain high-order exact penalty for nonconvex extremal problems in space Banach-valued absolutely functions. Using type distance function classes

We consider sequential quadratic programming methods (SQP) globalized by linesearch for the standard exact penalty function. It is well known that if the Hessian of the Lagrangian is used in SQP subproblems, the obtained direction may not be of descent for the penalty function. The reason is that the Hessian need not be positive definite, even locally, under any natural assumptions. Thus, if a ...

In this paper we present the continuous and discontinuous Galerkin methods in a unified setting for the numerical approximation of the transport dominated advection-reaction equation. Both methods are stabilized by the interior penalty method, more precisely by the jump of the gradient in the continuous case whereas in the discontinuous case the stabilization of the jump of the solution and opt...

We study stabilization methods for the discretization of convection-dominated elliptic convection-diffusion problems by linear finite elements. It turns out that there exist close relations between a new version of stabilization via local projection and the continuous interior penalty method. AMS Subject Classifications: 65 N15, 65N30, 65N12

We present an algorithm for large-scale equality constrained optimization. The method is based on a characterization of inexact sequential quadratic programming (SQP) steps that can ensure global convergence. Inexact SQP methods are needed for large-scale applications for which the iteration matrix cannot be explicitly formed or factored and the arising linear systems must be solved using itera...

This paper proposes a new method for real-time rigid body simulations based on a volumetric penalty method. The penalty method, which employs spring-damper model, is a simple and useful method for real-time simulation of multi-bodies. However, simple penalty method cannot handle face-face contact, because simple penalty method cannot find application point of reflection force. We suppose distri...

A family of problems for which the solution is a fixed size set is studied, using fitness functions with varying degrees of epistasis. An empirical comparison between a traditional crossover operator with a binary representation and a penalty function, and the representationindependent Random Assorting Recombination Operator (RAR) is performed. RAR is found to perform marginally better in all c...

If we believe that the two sequences x and y are similar then we might be able to optimally align them faster. For simplicity assume that m = n since our sequences are similar. If x and y align perfectly, then the optimal alignment corresponds to the diagonal in the dynamic programming table (now of size n × n). This is because all of the back pointers will be pointing diagonally. Therefore, if...

We formulate a penalty method for the obstacle problem associated with a nonlinear variational principle. It is proven that the solution to the relaxed variational problem (in both the continuous and discrete settings) is exact for finite parameter values above some calculable quantity. To solve the relaxed variational problem, an accelerated forward-backward method is used, which ensures conve...

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control over the desired level of sparsity of estimators. We analyze its structural properties and in doing so show the following: 1. Drawing parallels between robus...