The “relaxation” procedure introduced by Held and Karp for approximately solving a large linear programming problem related to the traveling-salesman problem is refined and studied experimentally on several classes ...
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The object of this paper is to prove duality theorems for quasiconvex programming problems. The principal tool used is the transformation introduced by Manas for reducing a nonconvex programming problem to a convex pr...
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The object of this paper is to prove duality theorems for quasiconvex programming problems. The principal tool used is the transformation introduced by Manas for reducing a nonconvex programming problem to a convex programming problem. Duality in the case of linear, quadratic, and linear-fractional programming is a particular case of this general case.
A nonlinear programming problem with inequality constraints and with unknown vector x is converted to an unconstrained minimization problem in unknowns x and lambda, where lambda is a vector of Lagrange multipliers. I...
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A nonlinear programming problem with inequality constraints and with unknown vector x is converted to an unconstrained minimization problem in unknowns x and lambda, where lambda is a vector of Lagrange multipliers. It is shown that, if the original problem possesses standard convexity properties, then local minima of the associated unconstrained problem are in fact global minima of that problem and, consequently, Kuhn-Tucker points for the original problem. A computational procedure based on the conjugate residual scheme is applied in the x lambda-space to solve the associated unconstrained problem. The resulting algorithm requires only first-order derivative information on the functions involved and will solve a quadratic programming problem in a finite number of steps.
In this study, we develop optimality criteria for a mathematical programming problem. The constraints are defined by an arbitrary set as welt as infinitely many equality and inequality constraints. Necessary condition...
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In this study, we develop optimality criteria for a mathematical programming problem. The constraints are defined by an arbitrary set as welt as infinitely many equality and inequality constraints. Necessary conditions of the Kuhn-Tucker type are obtained.
This paper deals with the behaviour of solutions to a linear fractional programming problem when the coefficients of the objective function are allowed to vary.
This paper deals with the behaviour of solutions to a linear fractional programming problem when the coefficients of the objective function are allowed to vary.
The well-known integral transform$$i(r) = - \frac{1}{\pi }\int\limits_{x = r}^1 {\frac{{dI(x)}}{{\sqrt {x^2 - r^2 } }},} 0 \leqq r \leqq 1,I(1) = 0$$ arising in spectroscopy, corresponds to half-order differentiation ...
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The well-known integral transform$$i(r) = - \frac{1}{\pi }\int\limits_{x = r}^1 {\frac{{dI(x)}}{{\sqrt {x^2 - r^2 } }},} 0 \leqq r \leqq 1,I(1) = 0$$ arising in spectroscopy, corresponds to half-order differentiation by substitutingr2 = 1 −s,x2 = 1 − t. Therefore noise is amplified by transforming the measured functionI intoi. Two undesirable effects may arise: (a) lack of smoothness ini (r), (b) intervals in whichi(r) < 0, although for physical reasons we should havei(r) ≧ *** developing a heuristic theory of noise amplification we present a fitting technique for approximate computation ofi(r), using the extra informationi(r) ≧ 0 as a restriction. This leads to a quadratic programming problem.
This paper describes a proposed special algorithm for a certain class of partionable linear programming problems. The matrix defining such a linear programming problem consists of a number of non-zero diagonal blocks,...
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This paper describes a proposed special algorithm for a certain class of partionable linear programming problems. The matrix defining such a linear programming problem consists of a number of non-zero diagonal blocks, plus some entirely filled rows and dito columns.
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