We propose a method to solve nonlinear second-order cone programs (SOCPs), based on a continuously di erentiable exact penalty function. The construction of the penalty function is given by incorporating a multipliers estimate in the augmented Lagrangian for SOCPs. Under the nondegeneracy assumption and the strong second-order su cient condition, we show that a generalized Newton method has glo...

This paper addresses the need for nonlinear programming algorithms that provide fast local convergence guarantees no matter if a problem is feasible or infeasible. We present an active-set sequential quadratic programming method derived from an exact penalty approach that adjusts the penalty parameter appropriately to emphasize optimality over feasibility, or vice versa. Conditions are presente...

Constrained global optimization problems can be tackled by using exact penalty approaches. In a preceding paper, we proposed an exact penalty algorithm for constrained problems which combines an unconstrained global minimization technique for minimizing a non-differentiable exact penalty function for given values of the penalty parameter, and an automatic updating of the penalty parameter that ...

A fast Newton method is proposed for solving linear programs with a very large (≈ 10) number of constraints and a moderate (≈ 10) number of variables. Such linear programs occur in data mining and machine learning. The proposed method is based on the apparently overlooked fact that the dual of an asymptotic exterior penalty formulation of a linear program provides an exact least 2-norm solution...

The problem of minimizing the number of misclassified points by a plane, attempting to separate two point sets with intersecting convex hulls in n-dimensional real space, is formulated as a linear program with equilibrium constraints (LPEC). This general LPEC can be converted to an exact penalty problem with a quadratic objective and linear constraints. A Frank-Wolfe-type algorithm is proposed ...

The problem of minimizing the number of misclassiied points by a plane, attempting to separate two point sets with intersecting convex hulls in n-dimensional real space, is formulated as a linear program with equilibrium constraints (LPEC). This general LPEC can be converted to an exact penalty problem with a quadratic objective and linear constraints. A Frank-Wolfe-type algorithm is proposed f...

One of the strengths of Model Predictive Control (MPC) is its ability to incorporate constraints in the control formulation. Often a disturbance drives the system into a region where the MPC problem is infeasible and hence no control action can be computed. Feasibility can be recovered by softening the constraints using slack variables. This approach does not necessarily guarantee that the cons...