In this paper, we give an overview on optimality conditions and exact penalization for the mathematical program with switching constraints (MPSC). MPSC is a new class of optimization problems important applications. It well known that if treated as standard nonlinear program, some usual constraint qualifications may fail. To deal issue, one could reformulate it disjunctive (MPDC). first survey ...

Gould and Robinson (NAR 08/18, Oxford University Computing Laboratory, 2008) gave global convergence results for a second-derivative SQP method for minimizing the exact l1-merit function for a fixed value of the penalty parameter. To establish this result, we used the properties of the so-called Cauchy step, which was itself computed from the so-called predictor step. In addition, we allowed fo...

This paper considers a finite element approximation of the Dirichlet problem for a second order self-adjoint elliptic equation, A u =f, in a region f 2 c N " (n=2 or 3) by the boundary penalty method. If the finite element space defined over D h, a union of elements, has approximation power h ~ in the L 2 norm, then (i) for f2=D h convex polyhedral, we show that choosing the penalty parameter e...

The symmetric interior penalty (SIP) method on graded meshes and its fast solution by multigrid methods are studied in this paper. We obtain quasi-optimal error estimates in both the energy norm and the L2 norm for the SIP method, and prove uniform convergence of the W -cycle multigrid algorithm for the resulting discrete problem. The performance of these methods is illustrated by numerical res...

In this paper, a new method called the OSCAR (Octagonal Shrinkage and Clustering Algorithm for Regression) is proposed to simultaneously select variables and perform supervised clustering in the context of linear regression. The technique is based on penalized least squares with a geometrically intuitive penalty function that, like the LASSO penalty, shrinks some coefficients to exactly zero. A...

In this paper we consider three embeddings (one-parametric optimization problems) motivated by penalty, exact penalty and Lagrange multiplier methods. We give an answer to the question under which conditions these methods are successful with an arbitrarily chosen starting point. Using the theory of one-parametric optimization (the local structure of the set of stationary points and of the set o...

We propose two line search primal-dual interior-point methods that approximately solve a sequence of equality constrained barrier subproblems. To solve each subproblem, our methods apply a modified Newton method and use an `2-exact penalty function to attain feasibility. Our methods have strong global convergence properties under standard assumptions. Specifically, if the penalty parameter rema...

In this paper, we will study optimality conditions of semi-infinite programs and generalized semi-infinite programs, for which the gradient objective function when evaluated at any feasible direction for the linearized constraint set is non-negative. We consider three types of penalty functions for semi-infinite program and investigate the relationship among the exactness of these penalty funct...