The paper discusses three general classes of nonlinear programming models. Our objective is to show how to represent optimization problem, such as nonlinear programs, in a compact format using extended mathematical programming. This is a useful tool, especially in cases when complementarity...

For univariate functions, we compute optimal breakpoint systems subject to the condition that the piecewise linear approximation (or, under- and overestimator) never deviates more than a given δ-tolerance from the original function, over a given finite interval. The linear approximators, under-...

The set of optimization problems in electric power systems engineering known collectively as Optimal Power Flow (OPF) is one of the most practically important and well-researched subfields of constrained nonlinear optimization. OPF has enjoyed a rich history of research, innovation, and...

Proper planning and management of irrigation is vital in achieving food security for the burgeoning global population and sustaining livelihoods. Because irrigated agriculture is expected to provide more food, if managed properly. The comprehensive reviews on the use of various programming...

In the analytic hierarchy process (AHP), Saaty's consistency index is performed to ensure that the preference information, provided in an individual judgement matrix, is neither random nor illogical. Based on the extension of Saaty's consistency index, this paper proposes a consensus index to...

We consider the problem of minimizing a smooth function over a feasible set defined as the Cartesian product of convex compact sets. We assume that the dimension of each factor set is huge, so we are interested in studying inexact block coordinate descent methods (possibly combined with column...

Robust optimization problems, which have uncertain data, are considered. We prove surrogate duality theorems for robust quasiconvex optimization problems and surrogate min–max duality theorems for robust convex optimization problems. We give necessary and sufficient constraint qualifications...

Loyalty programs, as a prevalent CRM strategy, aim to enhance customers’ loyalty and thereby increase a firm’s long-term profitability. Recent analytical and empirical studies demonstrate inconsistent findings on the efficacy of loyalty programs in fulfilling these goals. In this study, an...

In this study, the optimal burn time for low-thrust impulsive propulsion systems is investigated to raise the perigee altitude of a low-Earth orbit. The maneuver is done using spin-stabilized attitude control and impulsive thrusting system for a time interval centered about apogee point. On the...

Over the last few decades several methods have been proposed for handling functional constraints while solving optimization problems using evolutionary algorithms (EAs). However, the presence of equality constraints makes the feasible space very small compared to the entire search space. As a...