Optimization successive linear programming

Lagrange multiphers for, 2553-2554 and nonsmooth optimization, 2562 quadratic programming problems, 2555, 2562 separable programming problems, 2556-2558 sequential unconstrained minimization techniques for, 2560-2562 successive linear programming, 2562 successive quadratic programming, 2562 Constraint(s) ... 

Emphasis is placed in this chapter on the usage of process simulators to carry out the optimization simultaneously with converging the recycle loops and/or decision variables. To do the optimization efficiently, simulators use one of three methods (1) successive linear programming (SLP), (2) successive quadratic programming (SQP), and (3) generalized reduced gradient (GRG). Emphasis in this chapter is placed on SQP, used by ASPEN PLUS and HYSYS.Plant. GRG, which is used by CHEMCAD, is not discussed here, but is covered by Edgar et al. (2001). 

Chapter 13 illustrates the problem of constrained optimization by introducing the active set methods. Successive linear programming (SLP), projection, reduced direction search, SQP methods are described, implemented, and adopted to solve several practical examples of constrained linear/nonlinear optimization, including the solution of the Maratos effect. 

As pointed out by Kim et al. (1990), the difference between this algorithm and that of Patino-Leal is that the successive linearization solution is replaced with the nonlinear programming problem in Eq. (9.23). The nested NLP is solved as a set of decoupled NLPs, and the size of the largest optimization problem to be solved is reduced to the order of n. 

One special type of optimization problem involving restrictions or constraints has been solved quite successfully by a technique known as linear programming. From a mathematical viewpoint the basic form of the problem may be stated very briefly. Consider a linear response function of n variables ... 

Two types of nonlinear optimizers—the sectionalized linear program and the gradient search—have been successfully implemented in advanced computer control schemes. 

Any reasonable set of branching moves can be combined with any convenient relaxation to produce a branch and bound procedure. StiU, the great majority of successful applications and all commercial codes for discrete optimization use implementations of branch and bound on integer linear programs (ILP), with linear programming relaxations. The main ideas of such an algorithm can be outlined as follows ... 

Non-linear programming technique (NLP) is used to solve the problems resulting from syntheses optimisation. This NLP approach involves transforming the general optimal control problem, which is of infinite dimension (the control variables are time-dependant), into a finite dimensional NLP problem by the means of control vector parameterisation. According to this parameterisation technique, the control variables are restricted to a predefined form of temporal variation which is often referred to as a basis function Lagrange polynoms (piecewise constant, piecewise linear) or exponential based function. A successive quadratic programming method is then applied to solve the resultant NLP. 

Based on the given probabilities of success for each potential product, the problem is then to find the optimal product portfolio and investment decisions together with detailed production and sales plans so as to maximise the eNPV. The eNPV is simply the summation of all scenario NPVs, weighted by their associated probabilities. The derivation of the objective function is similar to the one in Papageorgiou et al. (2001). The overall problem is formulated as a two-stage, multi-scenario mixed integer linear programming (MILP) model. 

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