Titlebook: Mathematical Programming and Control Theory; B. D. Craven Book 1978 B. D. Craven 1978 Linear Programming.algorithms.mathematical programmi

物质

Fractional and complex programming,/.(.), of two functions. Such a problem is called a .. In particular, it is a . if . and . are linear, or affine, functions, and the constraints are linear. Although such problems are particular cases of nonlinear programming problems, stronger results for fractional programming problems are obtaina

努力赶上

Some algorithms for nonlinear optimization,simplex method for linear programming (3.3) is a highly efficient algorithm; while the number of iterations required to reach an optimum varies widely from one problem to another, the . number of iterations, for problems with constraints . — . ∈ ∝m/+ with . an . x . matrix with . much greater than .

消息灵通

Mathematical techniques,.. In particular, co .is the straight-line segment [x, y] joining the points . and .. A set . ⊂ . is convex if [x, y] ⊂ . whenever . ⊂.. (Equivalently, by an induction on the number of points, . is convex iff . = co ..)

上坡

GLADE

the variables. In the quarter century since G. B. Dantzig introduced the simplex method for linear programming, many real-world problems have been modelled in mathematical programming terms. Such problems often arise in economic planning - such as scheduling industrial production or transportation -

大骂

Optimization problems; Introduction,imum’ problems of the calculus textbooks, because the variables of the problem are nearly always subject to restrictions — equations or inequalities — called .. It is therefore not enough to equate a derivative, or gradient, to zero to find a maximum or minimum.

服从

Lagrangean theory,4.7) requiring also differentiable functions. The optimal dual variables can be interpreted as shadow costs, as in linear programming. Unlike linear programming, a dual of a nonlinear problem is not always unique; and the given (primal) problem is not always recovered as a dual of a dual (except under restrictions — see 4.8).

LUMEN

使闭塞

Some algorithms for nonlinear optimization,y the most efficient procedure. In particular, a problem which allows an adequate approximation by piece- wise linear functions, of not too many variables, may be computed as a . problem (3.4). Also a problem with a quadratic objective and linear constraints can be solved by a modified simplex method (4.6 and 7.6).

V洗浴

Linear systems,tion of a finite number of closed halfspaces); since linear implies convex, any local minimum is a global minimum; if . is nonempty and bounded, thus compact, then a minimum of (LP) is attained, at one of the finite number of extreme points of . (see 2.1). Note that (LP) may be re- written with constraints ..