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Linear fractional programming
Nonlinear fractional programming
4 other sections not shown
affine function applied assumed B. D. Craven chapter component computed concave function concave-convex fractional program Consider constant constraint qualification holds convergence convex function convex set denotes dual problem dual program eigenvalue example feasible point feasible set follows function f given gradient Hence hypotheses inequalities invex Karush-Kuhn-Tucker conditions Karush-Kuhn-Tucker necessary conditions KKT conditions Lagrange multiplier Lagrangian Lagrangian dual LFex linear constraints linear fractional program linear program linesearch Martos Mathematical Programming matrix Maximize f(x Maximize N(x)/D(x Minimize minimum NLF3 nonlinear fractional program Nonlinear Programming Note objective function Operations Research optimum parameter program NLF programming problem Proof Let properties pseudoconcave pseudoconvex quadratic program quasiconvex quasimax quasimin ratio reaches a maximum replaced Research Logistics Quarterly Schaible search direction sequence simplex algorithm simplex method stationary point strong dual subject to g(x Theorem TNLF+ TNLF2 unconstrained variables vector vTg(u weak duality weak maxima x e Rn XTg(x