Generalization of Geometric Programming: Partial Control of Linear Inventory Systems |
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A₁ A₂ auxiliary primal problem C₁ C₂ canonical form chemical elements chemical equilibrium problem chemical system components concave function constraints Eq convex D₁ D₂ degrees of difficulty domain D defined dual constraints dual problem dual variables duality relation Duffin-Zener type equal equations equilibrium constant equivalent free energy function Eq Geometric Inequality geometric programming problem given by Eq Hessian matrix independent variable Lagrange multipliers Lagrangian form linear inventory systems local maximum mathematical programming matrix maximization maximum minimization problem minimum mole necessary conditions non-negative notation objective function optimal optimum orthogonal P₁ P₁(t phase polynomials possible primal constraints primal function primal program primal variables probability of satisfactory Proof pseudo-maximum point pseudo-optimum points reactor saddle point satisfactory operation satisfies the necessary satisfy Eq Section signum function solution solved species STANFORD LIBRARIES t₁ t₂ temperature transformed unconstrained vector y₁