nonlinear programming

In this paper, we propose a novel and straightforward nonlinear programming approach for aggregating individual composite indicators (CIs) into a group-level composite indicator (e.g., an aggregate CI for a group of entities). Drawing on performance measurement literature, our model is designed to be both simple and computationally efficient, requiring no specialized solvers for implementation. The proposed approach addresses the growing need for robust and interpretable methods to synthesize multidimensional data, particularly in contexts where policymakers and researchers aim to compare and benchmark the performance of groups or regions. To demonstrate the practical application of our method, we compute an aggregate Human Development Index (HDI) for the European Union (EU) region using HDI sub-indicators from individual EU member states. This case study highlights the model’s ability to integrate diverse dimensions of human development—such as health, education, and standard of living—into a single, coherent metric. By doing so, we provide a tool for evaluating the collective progress of the EU region while preserving the unique contributions of each member state. Our approach offers several advantages: (1) it is computationally accessible, making it suitable for a wide range of applications; (2) it allows for flexibility in weighting and aggregation, accommodating diverse policy priorities; and (3) it provides a transparent framework for constructing group-level CIs, enhancing their utility for decision-making and public communication.

In this article, the Chebyshev pseudo-spectral (CPS) method is presented for solving Troesch’s problem, which is a singular, highly sensitive, and nonlinear boundary problem and occurs in the consideration of the confinement of a plasma column by radiation pressure. Here, a continuous time optimization (CTO) problem corresponding to Troesch’s problem is first proposed. Then, the Chebyshev pseudo-spectral method is used to convert the CTO problem to a discrete-time optimization problem its optimal solution can be found by nonlinear programming methods. The feasibility and convergence of the generated approximate solutions are analyzed. The proposed method is used to solve various kinds of Troesch’s equations. The obtained results have been compared with approximate solutions resulting from well known numerical methods. It can be confirmed that the numerical solutions resulting from this method are completely acceptable and accurate, compared with other techniques.

The roots of a polynomial have many applications in various sciences. If the polynomial under study has a degree of 4 or more, it will be impossible to find its roots through the coefficients. In this situation, most researchers use numerical methods to find the roots. The purpose of this research is to introduce a relatively simple method for calculating the real roots of a polynomial. In fact, the proposed approach emphasizes the ability of operation research science in the area of finding roots. In the end, some numerical examples are solved with the help of lingo software to better understand the proposed method. The results indicated that the proposed method is remarkably effective in finding the roots of a polynomial.

We formulate a new bond portfolio optimization model as a two-stage stochastic programming problem in which a decision maker can optimize the cost of bond portfolio selection while deciding which bonds to sell, which bonds to hold, and which bonds to buy from the market, as well as determine the quantity of additional cash in period t under different scenarios and varying assumptions, The model proved its efficiency by finding the optimal values and giving an investment plan that, it will reduce the cost of the portfolio.

This paper proposes a nonlinear programming model for a scheduling problem in the supply chain. Due to the nonlinear structure of the developed model and its NP-hard structure, a lower bound is developed. Four lemmas and a theorem are presented and proved to determine the lower bound. The proposed problem is inspired from a three stage supply chain commonly used in various industries.

‎The objective of the classical version of the minisum circle location problem is finding a circle $C$ in the plane such that the sum of the weighted distances from the circumference of $C$ to a set of given points is minimized‎, ‎where every point has a positive weight‎. ‎In this paper‎, ‎we investigate the semi-obnoxious case‎, ‎where every existing facility has either a positive or negative weight‎. ‎The distances are measured by the Euclidean norm‎. ‎Therefore‎, ‎the problem has a nonlinear objective function and global nonlinear optimization methods are required to solve this problem‎. ‎Some properties of the semi-obnoxious minisum circle location problem with Euclidean norm are discussed‎. ‎Then a cuckoo optimization algorithm is presented for finding the solution of this problem‎.

Challenges such as advances in technology, demands of the global market, and limited warehouse spaces resort manufacturing industries to subcontracting. Subcontracting has been a considerable alternative in the manufacturing industries and is utilized as a strategic tool to diminish operation costs primarily to address the problem of scarcity when the firm faces a large demand on the commodity it supplies. The present study employed a mathematical model among firms engaging in subcontracting in search of an optimal schedule in the manufacture of the product and distribution of production time involved with an objective of obtaining a maximum profit. The constraints in the mathematical formulation included the total demand, processing capacity, available supply, processing rate, and time. The plausibility and the possible utility of the mathematical model has been explored employing sequential quadratic programming algorithm in the search of the optimal solutions.

Optimization of the product portfolio has been recognized as a critical problem in industry, management, economy and so on. It aims at the selection of an optimal mix of the products to offer in the target market. As a probability function, reliability is an essential objective of the problem which linear models often fail to evaluate it. Here, we develop a multiobjective integer nonlinear constraint model for the problem. Our model provides opportunities to consider the knowledge transferring cost and the environmental effects, as nowadays important concerns of the world, in addition to the classical factors operational cost and reliability. Also, the model is designed in a way to simultaneously optimize the input materials and the products. Although being to some extent complicated, the model can be efficiently solved by the metaheuristic algorithms. Finally, we make some numerical experiments on a simulated test problem.

This paper introduces the \emph{interval unilateral quadratic matrix equation}, \IUQe and attempts to find various analytical results on its AE-solution sets in which \A,\B and \CCC are known real interval matrices, while X is an unknown matrix. These results are derived from a generalization of some results of Shary. We also give sufficient conditions for non-emptiness of some quasi-solution sets, provided that \A is regular. As the most common case, the united solution set has been studied and two direct methods for computing an outer estimation and an inner estimation of the united solution set of an interval unilateral quadratic matrix equation are proposed. The suggested techniques are based on nonlinear programming as well as sensitivity analysis.