Nonlinear Optimization with Engineering Applications

Abstract

Aims and ScopeOptimization has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics and other sciences.The Springer Series in Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository works that focus on algorithms for solving optimization problems and also study applications involving such problems. Some of the topics covered include nonlinear optimization (convex and nonconvex), network flow problems, stochastic optimization, optimal control, discrete optimization, multiobjective programming, description of software packages, approximation techniques and heuristic approaches.

Optimizing Omega

“…It is well-known (see for instance [3]) that the minimum of the exact penalty function (9) coincides with the solution of the original inequality constrained problem provided ρ is chosen sufficiently large.…”

“…(see [3] for instance). Table 4 shows the portfolios obtained by minimizing downside risk DV for the values of R p in Tables 2 and 3.…”

Some mathematical aspects of price optimisation

“…The most popular method discussed in the literature for solving this type of optimisation problem is the Sequential Quadratic Programming method (SQP), see [15,16,17]. It is an iterative method that generates a sequence of quadratic programs to be solved at each iterate.…”

Fuzzy Preferences in the Graph Model for Conflict Resolution

“…It ranges from simple everyday decisions to strategic decisions in war. To make decisions easier, a number of methodologies have been developed, including linear and non-linear optimization (Bartholomew-Biggs, 2008;Chang, 2010;Taha, 1971), multiple-criteria decision analysis (MCDA) (Chang, 2010;Figueira et al, 2005;Hipel et al, 1993b), game theory (von Neumann and Morgenstern, 1944), fuzzy decision making (Nakamura, 1986;De Wilde, 2004), and the Graph Model for Conflict Resolution (GMCR) (Fang et al, 1993;Kilgour et al, 1987). Depending on the number of decision makers (DMs) and objectives, decision making techniques are divided into four main categories: (i) single participant-single objective (such as most operations research models), (ii) single participant-multiple objective (such as MCDA methods), (iii) multiple participant-single objective (such as team theory), and (iv) multiple participantmultiple objective (such as GMCR) decision making.…”