Nonlinear Programming II: Unconstrained Optimization Techniques

Evolutionary computation techniques have received a great deal of attention regarding their potential as optimization techniques for complex numerical functions. However, they have not produced a significant breakthrough in the area of nonlinear programming due to the fact that they have not addressed the issue of constraints in a systematic way. Only recently have several methods been proposed for handling nonlinear constraints by evolutionary algorithms for numerical optimization problems; however, these methods have several drawbacks, and the experimental results on many test cases have been disappointing. In this paper we (1) discuss difficulties connected with solving the general nonlinear programming problem; (2) survey several approaches that have emerged in the evolutionary computation community; and (3) provide a set of 11 interesting test cases that may serve as a handy reference for future methods.

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Introduction to Optimization Techniques: Fundamentals and Applications of Nonlinear Programming.

Journal of the Royal Statistical Society Series C (Applied Statistics) ◽

10.2307/2346496 ◽

1972 ◽

Vol 21 (2) ◽

pp. 208

Author(s):

E. M. L. Beale ◽

Masanao Aoki

Keyword(s):

Nonlinear Programming ◽

Optimization Techniques

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First-order unconstrained optimization techniques

Nonlinear Optimization in Electrical Engineering with Applications in MATLAB® ◽

10.1049/pbsp008e_ch6 ◽

2013 ◽

pp. 153-174

Keyword(s):

Unconstrained Optimization ◽

Optimization Techniques ◽

First Order

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Integrated Optimal Design of Planar Mechanisms Using Fuzzy Theories

15th Design Automation Conference: Volume 2 — Design Optimization ◽

10.1115/detc1989-0086 ◽

1989 ◽

Author(s):

A. K. Dhingra ◽

S. S. Rao

Keyword(s):

Nonlinear Programming ◽

High Speed ◽

Integrated Approach ◽

Problem Formulation ◽

Optimization Techniques ◽

Motion Path ◽

Programming Formulation ◽

Planar Mechanisms ◽

Dynamic Synthesis ◽

Motion Characteristics

Abstract A new integrated approach to the design of high speed planar mechanisms is presented. The resulting nonlinear programming formulation combines both the kinematic and dynamic synthesis aspects of mechanism design. The multiobjective optimization techniques presented in this work facilitate the design of a linkage to meet several kinematic and dynamic design criteria. The method can be used for motion, path, and function generation problems. The nonlinear programming formulation also permits the imposition of constraints to eliminate solutions which possess undesirable kinematic and motion characteristics. To model the vague and imprecise information in the problem formulation, the tools of fuzzy set theory have been used. A method of solving the resulting fuzzy multiobjective problem using mathematical programming techniques is presented. The outlined procedure is expected to be useful in situations where doubt arises about the exactness of permissible values, degree of credibility, and correctness of statements and judgements.

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