Anthony V. Fiacco

Nonlinear programming : sequential unconstrained minimization techniques

Abstract : This report gives the most comprehensive and detailed treatment to date of some of the most powerful mathematical programming techniques currently known--sequential unconstrained methods for constrained minimization problems in Euclidean n-space--giving many new results not published elsewhere. It provides a fresh presentation of nonlinear programming theory, a detailed review of other unconstrained methods, and a development of the latest algorithms for unconstrained minimization. (Author)

The Slacked Unconstrained Minimization Technique for Convex Programming

An algorithm for solving the problem: minimize

The Sequential Unconstrained Minimization Technique (SUMT) Without Parameters

f( x )

Second Order Sufficient Conditions for Weak and Strict Constrained Minima

(a convex function) subject to

GENERALIZED PENALTY METHODS IN TOPOLOGICAL SPACES

g_i ( x )\geqq 0

PROGRAMMING UNDER NONLINEAR CONSTRAINTS BY UNCONSTRAINED MINIMIZATION: A PRIMAL-DUAL METHOD,

,

COMPUTER PROGRAM IMPLEMENTING THE SEQUENTIAL UNCONSTRAINED MINIMIZATION TECHNIQUE FOR NONLINEAR PROGRAMMING.

i = 1, \cdots ,m

THE SEQUENTIAL UNCONSTRAINED MINIMIZATION TECHNIQUE FOR CONVEX PROGRAMMING WITH EQUALITY CONSTRAINTS.

, each

ASYMPTOTIC CONDITIONS FOR CONSTRAINED MINIMIZATION.

g_i

A General Regularized Sequential Unconstrained Minimization Technique

a concave function, is presented. Specifically, the function \[ P\left[ {x,t,r_k } \right] \equiv f( x ) + r_k^{ - 1} \sum {\left[ {g_i ( x ) - t_i } \right]} ^2 \] is minimized over all x, nonnegative t, for a strictly decreasing null sequence