A compact variable metric algorithm for linearly constrained nonlinear minimax approximation
A comparative study on optimization methods for the constrained nonlinear programming problems.
A Constraint Linearization Method for Nondifferentiable Convex Minimization.
A convergent algorithm for solving linear programs with an additional reverse convex constraint
A General Convergence Theorem for the Reduced Gradient Method.
A hybrid inertial projection-proximal method for variational inequalities.
A modified filter SQP method as a tool for optimal control of nonlinear systems with spatio-temporal dynamics
Our aim is to adapt Fletcher's filter approach to solve optimal control problems for systems described by nonlinear Partial Differential Equations (PDEs) with state constraints. To this end, we propose a number of modifications of the filter approach, which are well suited for our purposes. Then, we discuss possible ways of cooperation between the filter method and a PDE solver, and one of them is selected and tested.
A new one-step smoothing newton method for second-order cone programming
In this paper, we present a new one-step smoothing Newton method for solving the second-order cone programming (SOCP). Based on a new smoothing function of the well-known Fischer-Burmeister function, the SOCP is approximated by a family of parameterized smooth equations. Our algorithm solves only one system of linear equations and performs only one Armijo-type line search at each iteration. It can start from an arbitrary initial point and does not require the iterative points to be in the sets...
A note on necessary conditions in mathematical programming
A Numerical Method for Detecting Singular Minimizers.
A Regularized Continuous Projection-Gradient Method of the Fourth Order
A self-adaptive method for solving a system of nonlinear variational inequalities.
A sensitivity-based extrapolation technique for the numerical solution of state-constrained optimal control problems
Sensitivity analysis (with respect to the regularization parameter) of the solution of a class of regularized state constrained optimal control problems is performed. The theoretical results are then used to establish an extrapolation-based numerical scheme for solving the regularized problem for vanishing regularization parameter. In this context, the extrapolation technique provides excellent initializations along the sequence of reducing regularization parameters. Finally, the favorable numerical behavior...
About the relation between some optimality conditions
The relation between the general optimality conditions in terms of contact cones and the Kuhn-Tucker conditions in the special case of pseudo-convex and quasi-convex functions and their consequence to Lagrangian multipliers are given.
An active set strategy based on the augmented Lagrangian formulation for image restoration
Lagrangian and augmented Lagrangian methods for nondifferentiable optimization problems that arise from the total bounded variation formulation of image restoration problems are analyzed. Conditional convergence of the Uzawa algorithm and unconditional convergence of the first order augmented Lagrangian schemes are discussed. A Newton type method based on an active set strategy defined by means of the dual variables is developed and analyzed. Numerical examples for blocky signals and images perturbed by...
An implementation of recursive quadratic programming variable metric methods for linearly constrained nonlinear minimax approximation
An inexact proximal-type method for the generalized variational inequality in Banach spaces.
An SQP method for mathematical programs with complementarity constraints with strong convergence properties
We propose an SQP algorithm for mathematical programs with complementarity constraints which solves at each iteration a quadratic program with linear complementarity constraints. We demonstrate how strongly M-stationary solutions of this quadratic program can be obtained by an active set method without using enumeration techniques. We show that all limit points of the sequence of iterates generated by our SQP method are at least M-stationary.
Application of the optimal control theory to the wastewater elimination problem.
The main goal of this paper is to show some applications of the optimal control theory to the wastewater elimination problem. Firstly, we deal with the numerical simulation of a given situation. We present a suitable mathematical model, propose a method to solve it and show the numerical results for a realistic situation in the ría of Arousa (Spain). Secondly, in the same framework of wastewater elimination problem, we pose two economic-environmental problems which can be formulated as constrained...