This paper proposes a new step called the P-step to handle the linear or nonlinear equality constraint in addition to the conventional EM algorithm. This new step is easy to implement, first because only the first derivatives of the object function and the constraint function are necessary, and...

In this paper, for solving variational inequality problems (VIPs) we propose a feasible descent algorithm via minimizing the regularized gap function of Fukushima. Under the condition that the underlying mapping of VIP is strongly monotone, the algorithm is globally convergent for any...

A new smoothing approach was given for solving the mathematical programs with complementarity constraints (MPCC) by using the aggregation technique. As the smoothing parameter tends to zero, if the KKT point sequence generated from the smoothed problems satisfies the second-order necessary...

For semi-infinite programming (SIP), we consider a class of smoothed penalty functions, which approximate the exact $$l_\rho (0\rho \le 1)$$ penalty functions. On base of the smoothed penalty function, we present a feasible penalty algorithm for solving SIP. Without any boundedness condition or...

In this paper, the feasible type SQP method is improved. A new algorithm is proposed to solve nonlinear inequality constrained problem, in which a new modified method is presented to decrease the computational complexity. It is required to solve only one QP subproblem with only a subset of the...

The Order-Value Optimization (OVO) problem is a generalization of the classical Minimax problem. Instead of the maximum of a set functions, the functional value that ranks in the p-th place is minimized. The problem seeks the application to (non-pessimistic) decision making and to model fitting...

In this paper, a new trust region method is presented for general constrained optimization problem. In this algorithm, the trial step is obtained by solving two quadratic programming problems with bound constraints. The algorithm is implementable easily. Then we prove that the method is globally...

An active set limited memory BFGS algorithm for large-scale bound constrained optimization is proposed. The active sets are estimated by an identification technique. The search direction is determined by a lower dimensional system of linear equations in free subspace. The implementations of the...

The solution of an equation f(x)=γ given by an increasing function f on an interval I and right-hand side γ, can be approximated by a sequence calculated according to Newton’s method. In this article, global convergence of the method is considered in the strong sense of convergence for any...

In this paper, an extended form of the entropic perturbation method of linear programming is given, which can overcome the weakness of the original method – being easy of overflow in computing. Moreover, the global convergence of the gradient algorithm for the method is discussed. Copyright...