For a highly nonlinear programming (NLP) problem with fewer than 50 variables where gradients must be found numerically, which solution method is suggested as the best?
Explanation
Different NLP algorithms have different strengths. SQP is powerful for smaller, dense, highly nonlinear problems because it uses more information about the curvature of the function (a quadratic approximation) than SLP, leading to faster convergence.
Other questions
What is the first step in formulating an optimization problem?
According to Table 12.1, which of the following is typically an objective to be minimized in design optimization?
What is the source of equality constraints in an optimization model?
In a constrained optimization problem, what is an 'active' constraint?
In the optimization of process heat recovery, what is the typical range for the optimum minimum temperature approach, DToptimum?
What is the fundamental trade-off when optimizing the degree of process heat recovery?
Why might optimizing a subcomponent of a process, like a single distillation column, not lead to the optimum design for the whole process?
In a single-variable optimization problem, what does a second derivative of the objective function that is less than zero at a stationary point indicate?
The golden-section search is a single-variable search method that is more computationally efficient than a regular search if the desired precision fraction, epsilon, is below what value?
The golden-section search method reduces the search range to what fraction of the original range with each new point added?
What is the primary challenge associated with multivariable optimization problems that have a nonconvex feasible region?
In a linear programming (LP) problem, where is the optimal solution guaranteed to be located?
What is the role of slack and surplus variables in the SIMPLEX algorithm for linear programming?
What is a significant limitation of the successive linear programming (SLP) method for solving nonlinear problems?
In optimization problems, what is the purpose of introducing binary integer variables?
What is the name of the algorithm commonly used for solving mixed-integer problems that works by treating integer variables as continuous and then systematically partitioning the problem?
Which of the following is cited as a reason why few industrial designs are rigorously optimized?
In the distillation column optimization in Example 12.1, what was the total annualized cost (TAC) for the initial guess of 40 trays with the feed on tray 20?
What was the 'soft constraint' on the column height in the optimization of the distillation column in Example 12.1?
In Example 12.1, what was the final optimized design for the distillation column in terms of the number of trays and feed tray location?
What was the final total annualized cost for the optimized distillation column design of 80 trays with feed on tray 27 in Example 12.1?
When investigating the feasibility of a 120-tray column in Example 12.1, what installation factor was used for the column shell to account for the higher cost of using larger cranes?
In an optimization problem expressed as 'Optimize z = f(x)', what does the function f(x) represent?
An optimization problem is described as 'unbounded' when what condition occurs?
If an optimization problem has 'n' variables and 'me' equality constraints, how are the degrees of freedom determined?
The quasi-Newton method is an indirect search method that finds an optimum by searching for a point that satisfies which condition?
In the steepest descent method for multivariable optimization, what determines the search direction from the current point?
What is a 'degenerate' linear programming (LP) problem?
For which type of nonlinear programming (NLP) problems are reduced gradient methods noted to be particularly effective?
What is the goal of superstructure optimization in process synthesis?
In Example 12.1, what rule of thumb was applied to convert the installed capital cost of the distillation column into an annual capital charge?
What were the specified costs per Gigajoule (GJ) for heating and cooling utilities in the distillation column optimization of Example 12.1?
In the second iteration of the distillation column optimization in Example 12.1 (90 trays), what were the calculated column height and total annualized cost?
In Example 12.1, why was the initial 40-tray design considered suboptimal?
Why is Discounted Cash Flow Rate of Return (DCFROR) described as an intrinsically difficult optimization objective?
What is a potential issue with using Net Present Value (NPV) as an optimization objective?
When optimizing a single variable that is bounded by constraints, what must be checked in addition to stationary points?
What property defines a convex feasible region in multivariable optimization?
Which class of methods can be used to overcome the problem of an optimization algorithm converging to a local optimum?
In which two industrial areas are operations research methods like LP and MILP widely used?
For batch and semicontinuous processes that have nonproductive periods, what is typically optimized to find the minimum cost per unit of production?
Which of the following is listed as one of the most important things for a design engineer to understand when performing industrial process design optimization?
What is a key difference in the number of new points calculated per cycle between a regular three-point interval search and a golden-section search?
In the 90-tray design for the distillation column in Example 12.1, what were the calculated reflux ratio and column diameter?
What was the approximate total annualized cost savings in Example 12.1 when moving from the initial 40-tray design to the improved 90-tray design?
What is the term for a problem where the feasible region defined by the constraints has no solution?
Why must the boundaries of the search space be checked when optimizing a single-variable function?
Which optimization method involves approximating the objective function as a quadratic function and is well-suited for highly nonlinear problems with relatively few variables?
What type of optimization problem results when discrete variables are introduced into a nonlinear program (NLP)?