The Algebraic Degree of Geometric Optimization Problems.
The Convergence of Matrices Generated by Rank-2 Methods from the Restricted ß-Class of Broyden.
The Duoplex-Algorithm.
The expected-projection method: Its behavior and applications to linear operator equations and convex optimization.
The Lagrange multipliers theorem for locally convex metric spaces
The Largest Subdeterminant of a Matrix
The minimum value of as the quality control criterion
The new iteration methods for solving absolute value equations
Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we propose two new iteration methods for solving absolute value equations , where is an -matrix or strictly diagonally dominant matrix, and is an unknown solution vector. Furthermore, we discuss the convergence of the proposed two methods under suitable assumptions. Numerical experiments are given to verify the feasibility, robustness and effectiveness...
The Nonlinear Programming Method of Wilson, Han, and Powell with an Augmented Lagrangian Type Line Search Function. Part 1 : Convergence Analysis.
The Nonlinear Programming Method of Wilson, Han, and Powell with an Augmented Lagrangian Type Line Search Function. Part 2 : An Efficient Implementation with Linear Least Squares Subproblems.
The optimization of heat radiation intensity
This article focuses on the problem of calculating the intensity of heat radiation and its optimization across the surface of an aluminium or nickel mould. The inner mould surface is sprinkled with a special PVC powder and the outer mould surface is warmed by infrared heaters located above the mould. In this way artificial leathers are produced in the car industry (e.g., the artificial leather on a car dashboard). The article includes a description of how a mathematical model allows us to calculate the...
The second order optimality conditions for nonlinear mathematical programming with data
To find nonlinear minimization problems are considered and standard -regularity assumptions on the criterion function and constrained functions are reduced to -regularity. With the aid of the generalized second order directional derivative for real-valued functions, a new second order necessary optimality condition and a new second order sufficient optimality condition for these problems are derived.
Théorie de la pénalisation exacte
Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification
The paper concerns the study of tilt stability of local minimizers in standard problems of nonlinear programming. This notion plays an important role in both theoretical and numerical aspects of optimization and has drawn a lot of attention in optimization theory and its applications, especially in recent years. Under the classical Mangasarian-Fromovitz Constraint Qualification, we establish relationships between tilt stability and some other stability notions in constrained optimization. Involving...
Tour d'horizon : programmation non linéaire