Monotonicity Analysis and Recursive Quadratic Programming in Constrained Optimization

1985 ◽  
Vol 107 (4) ◽  
pp. 459-462 ◽  
Author(s):  
J. Zhou ◽  
R. W. Mayne
Keyword(s):  
Quadratic Programming ◽  
Constrained Optimization ◽  
Nonlinear Optimization ◽  
Active Set ◽  
Active Set Strategy ◽  
Constrained Nonlinear Optimization ◽  
Recursive Quadratic Programming ◽  
Analysis Strategy ◽  
Original Procedure ◽  
Monotonicity Analysis

This paper considers the use of an active set strategy based on monotonicity analysis as an integral part of a recursive quadratic programming (RQP) algorithm for constrained nonlinear optimization. Biggs’ RQP method employing equality constrained subproblems is the basis for the algorithm developed here and requires active set information. The monotonicity analysis strategy is applied to the sequence of search directions selected by the RQP method. As each direction is considered, progress toward optimum occurs and a new constraint is added to the active set. As the active set is finalized the basic RQP method is followed unless a constraint is to be dropped. Testing of the proposed algorithm illustrates its promise as an enhancement to Biggs’ original procedure.

Optimization With Discrete Variables Via Recursive Quadratic Programming: Part 2—Algorithm and Results

1989 ◽  
Vol 111 (1) ◽  
pp. 130-136 ◽  
Author(s):  
J. Z. Cha ◽  
R. W. Mayne
Keyword(s):  
Quadratic Programming ◽  
Performance Comparison ◽  
Programming Algorithm ◽  
Discrete Variables ◽  
Contour Analysis ◽  
Recursive Quadratic Programming ◽  
Analysis Technique ◽  
Rank One ◽  
Symmetric Rank One ◽  
Monotonicity Analysis

A discrete recursive quadratic programming algorithm is developed for a class of mixed discrete constrained nonlinear programming (MDCNP) problems. The symmetric rank one (SR1) Hessian update formula is used to generate second order information. Also, strategies, such as the watchdog technique (WT), the monotonicity analysis technique (MA), the contour analysis technique (CA), and the restoration of feasibility have been considered. Heuristic aspects of handling discrete variables are treated via the concepts and convergence discussions of Part I. This paper summarizes the details of the algorithm and its implementation. Test results for 25 different problems are presented to allow evaluation of the approach and provide a basis for performance comparison. The results show that the suggested method is a promising one, efficient and robust for the MDCNP problem.

PRIMA: A Production-Based Implicit Elimination System for Monotonicity Analysis of Optimal Design Models

1991 ◽  
Vol 113 (4) ◽  
pp. 408-415 ◽  
Author(s):  
J. R. Rao ◽  
P. Y. Papalambros
Keyword(s):  
Optimal Design ◽  
Heuristic Search ◽  
Programming Environment ◽  
Initial Model ◽  
Active Set ◽  
Design Models ◽  
Active Set Strategy ◽  
Knowledge Based ◽  
Reasoning System ◽  
Monotonicity Analysis

Monotonicity analysis is a useful method for analyzing optimal design models prior to numerical computation. Much of the information required for such analysis is represented in the monotonicity table. Rigorous procedures using the monotonicity principles and the implicit function theorem have been combined with heuristics, to extract additional constraint activity knowledge based only on the information contained in the monotonicity table. PRIMA is a production system implemented in the OPS5 programming environment. The system receives as input the monotonicity table of the initial model and derives global facts about boundedness and constraint activity by heuristic search of sequences of successively reduced models. Such reduction is obtained by implicit elimination of active constraints. Global facts generated automatically by this reasoning system can be used either for a global solution, or for a combined local-global active set strategy.

An Automated Procedure for Local Monotonicity Analysis

1984 ◽  
Vol 106 (1) ◽  
pp. 82-89 ◽  
Author(s):  
S. Azarm ◽  
P. Papalambros
Keyword(s):  
Design Optimization ◽  
Active Set ◽  
Optimization Program ◽  
Active Set Strategy ◽  
Active Constraints ◽  
Automated Algorithm ◽  
Active Sets ◽  
Local Monotonicity ◽  
Monotonicity Analysis ◽  
Selection Of

A strategy for selecting active constraints in a design optimization program is implemented computationally. The strategy uses local monotonicity information to iterate on the active set. A fully automated algorithm is developed with the aid of constrained derivatives and conventional search methods. Four design examples are presented, one of which demonstrates how global rules derived from monotonicity analysis can be included in the active set strategy to enhance the performance of the algorithm. The procedure is flexible, so that any available rules that can bias the selection of active sets may be included in the strategy.

Constrained Nonlinear Optimization in Business

2014 ◽  
pp. 523-535
Author(s):  
William P. Fox
Keyword(s):  
Genetic Algorithm ◽  
Constrained Optimization ◽  
Nonlinear Optimization ◽  
Traveling Salesman Problem ◽  
Optimization Problems ◽  
Transportation Networks ◽  
Business Environment ◽  
Traveling Salesman ◽  
Constrained Nonlinear Optimization ◽  
The Traveling Salesman Problem

We present both classical analytical, numerical, and heuristic techniques to solve constrained optimization problems relating to business, industry, and government. We briefly discuss other methods such as genetic algorithm. Today's business environment has many resource challenges to their attempts to maximize profits or minimize costs for which constrained optimization might be used. Facility location and transportation networks techniques are often used as well as the traveling salesman problem.

Constrained Nonlinear Optimization in Information Science

2019 ◽  
pp. 705-721
Author(s):  
William P. Fox
Keyword(s):  
Constrained Optimization ◽  
Nonlinear Optimization ◽  
Information Science ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Smart Phones ◽  
Inequality Constrained Optimization ◽  
Constrained Nonlinear Optimization ◽  
Background Theory ◽  
Methods And Techniques

This chapter provides an overview of constrained optimization methods. Background, theory, and examples are provided. Coverage includes Lagrange multipliers for equality constrained optimization with a Cobb-Douglass example from information science. The authors also provide Karush-Kuhn-Tucker for inequality-constrained optimization and a production example for smart phones with inequalities. An overview and discussion of numerical methods and techniques is also provided. The authors also provide a brief list of technology available to assist in solving these constrained nonlinear optimization problems.

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