Optimization and Engineering 

About: Optimization and Engineering is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Optimization problem & Computer science. It has an ISSN identifier of 1389-4420. Over the lifetime, 906 publications have been published receiving 19922 citations.

A tutorial on geometric programming

Abstract: A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods can solve even large-scale GPs extremely efficiently and reliably; at the same time a number of practical problems, particularly in circuit design, have been found to be equivalent to (or well approximated by) GPs. Putting these two together, we get effective solutions for the practical problems. The basic approach in GP modeling is to attempt to express a practical problem, such as an engineering analysis or design problem, in GP format. In the best case, this formulation is exact; when this is not possible, we settle for an approximate formulation. This tutorial paper collects together in one place the basic background material needed to do GP modeling. We start with the basic definitions and facts, and some methods used to transform problems into GP format. We show how to recognize functions and problems compatible with GP, and how to approximate functions or data in a form compatible with GP (when this is possible). We give some simple and representative examples, and also describe some common extensions of GP, along with methods for solving (or approximately solving) them.

CVXGEN: a code generator for embedded convex optimization

Abstract: CVXGEN is a software tool that takes a high level description of a convex optimization problem family, and automatically generates custom C code that compiles into a reliable, high speed solver for the problem family. The current implementation targets problem families that can be transformed, using disciplined convex programming techniques, to convex quadratic programs of modest size. CVXGEN generates simple, flat, library-free code suitable for embedding in real-time applications. The generated code is almost branch free, and so has highly predictable run-time behavior. The combination of regularization (both static and dynamic) and iterative refinement in the search direction computation yields reliable performance, even with poor quality data. In this paper we describe how CVXGEN is implemented, and give some results on the speed and reliability of the automatically generated solvers.

Variations and extension of the convex–concave procedure

Abstract: We investigate the convex–concave procedure, a local heuristic that utilizes the tools of convex optimization to find local optima of difference of convex (DC) programming problems. The class of DC problems includes many difficult problems such as the traveling salesman problem. We extend the standard procedure in two major ways and describe several variations. First, we allow for the algorithm to be initialized without a feasible point. Second, we generalize the algorithm to include vector inequalities. We then present several examples to demonstrate these algorithms.

Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques

Abstract: This paper has as a major objective to present a unified overview and derivation of mixed-integer nonlinear programming (MINLP) techniques, Branch and Bound, Outer-Approximation, Generalized Benders and Extended Cutting Plane methods, as applied to nonlinear discrete optimization problems that are expressed in algebraic form. The solution of MINLP problems with convex functions is presented first, followed by a brief discussion on extensions for the nonconvex case. The solution of logic based representations, known as generalized disjunctive programs, is also described. Theoretical properties are presented, and numerical comparisons on a small process network problem.

A Coupled-Adjoint Sensitivity Analysis Method for High-Fidelity Aero-Structural Design

Abstract: This paper presents an adjoint method for sensitivity analysis that is used in an aero-structural aircraft design framework The aero-structural analysis uses high-fidelity models of both the aerodynamics and the structures Aero-structural sensitivities are computed using a coupled-adjoint approach that is based on previously developed single discipline sensitivity analysis Alternative strategies for coupled sensitivity analysis are also discussed The aircraft geometry and a structure of fixed topology are parameterized using a large number of design variables The aero-structural sensitivities of aerodynamic and structural functions with respect to these design variables are computed and compared with results given by the complex-step derivative approximation The coupled-adjoint procedure is shown to yield very accurate sensitivities and to be computationally efficient, making high-fidelity aero-structural design feasible for problems with thousands of design variables