In this paper, we consider a computational method of Stackelberg solutions for noncooperative two-level nonlinear programming problems (TLNLPPs) which contain two decision makers with different priorities. For the pur...
详细信息
This paper introduces and investigates new classes of weak fractional vector variational-like inequalities and fractional vector variational-like inequalities. We establish an equivalence between the efficient solutio...
详细信息
This paper introduces and investigates new classes of weak fractional vector variational-like inequalities and fractional vector variational-like inequalities. We establish an equivalence between the efficient solutions of fractional optimization problems and the solutions of introduced inequalities using a parametric approach under generalized invexity assumptions. By applying the KKM Lemma, we prove the existence of solutions for a fractional vector variational-like inequality problem. We also illustrate the derived results with examples. Additionally, we consider an application-based problem in portfolio allocation to validate our findings.
On the basis of Matlab mathematical tool, nonlinear programming function-fmincon is used to optimize and design allocation plan for radiological workers at strong radiation field in this paper, establishing correspond...
详细信息
A method of multiplier is presented for solving optimization problems. For large-scale constraint problems, combining the active set strategy, we use the aggregate function to approximate the max-value function. Only ...
详细信息
The electrical network reconfiguration problem aims to minimize losses in a distribution system by adjusting switches while ensuring the radiality (tree structure) of the network. Although this problem can be formulat...
详细信息
The electrical network reconfiguration problem aims to minimize losses in a distribution system by adjusting switches while ensuring the radiality (tree structure) of the network. Although this problem can be formulated as a mixed integer nonlinear program, solving the resulting optimization problem requires significant time and resources. A carefully selected initial solution, which can be identified by appropriate heuristics, reduces the search space, accelerates convergence, and ensures feasibility. This paper introduces two heuristic algorithms based on the Alternating Direction Method of Multipliers (ADMM) to address this problem. These heuristics break down the problem into smaller, more manageable subproblems that can be solved efficiently. Two algorithms are developed: one relies on natural variable substitution, and the other on a previously used relaxation technique. The challenge encountered in previous studies of incorporating radial constraints with ADMM is addressed by redefining the combinatorial subproblem in the projection step of ADMM as a minimum weight rooted arborescence problem, whose solutions are guaranteed to be radial. Convex optimization techniques can then handle the remaining subproblems. The performance of both heuristics is evaluated through numerical experiments on the 33-bus and 70-bus systems, as well as on a real-world electrical network.
In [R. J. Baraldi and D. P. Kouri, Mathematical programming, (2022), pp. 1-40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex and nonsmooth convex function. The principle...
详细信息
In [R. J. Baraldi and D. P. Kouri, Mathematical programming, (2022), pp. 1-40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex and nonsmooth convex function. The principle expense of this method is in computing a trial iterate that satisfies the so-called fraction of Cauchy decrease condition-a bound that ensures the trial iterate produces sufficient decrease of the subproblem model. In this paper, we expound on various proximal trust-region subproblem solvers that generalize traditional trust-region methods for smooth unconstrained and convex-constrained problems. We introduce a simplified spectral proximal gradient solver, a truncated nonlinear conjugate gradient solver, and a dogleg method. We compare algorithm performance on examples from data science and PDE-constrained optimization.
This paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in fi...
详细信息
This paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces. The established conditions are expressed in terms of second-order subdifferentials of lower semicontinuous functions and mainly concern proxregular objectives that cover a large territory in nonsmooth optimization and its applications. Our tools are based on the machinery of variational analysis and second-order generalized differentiation. The obtained general results are applied to problems of nonlinear programming, where the derived second-order optimality conditions are new even for problems with twice continuously differential data, being expressed there in terms of the classical Hessian matrices.
In this work, new mixed integer nonlinear optimization models are proposed for two clustering problems: the unitary weighted Weber problem and the minimum sum of squares clustering. The proposed formulations are conve...
详细信息
In this work, new mixed integer nonlinear optimization models are proposed for two clustering problems: the unitary weighted Weber problem and the minimum sum of squares clustering. The proposed formulations are convex quadratic models with linear and second-order cone constraints that can be efficiently solved by interior point algorithms. Their continuous relaxation is convex and differentiable. The numerical experiments show the proposed models are more efficient than some classical models for these problems known in the literature.
Global warming and population growth have significantly intensified the challenges in securing drinking water supplies. This study investigates transient instabilities of streamflow using ensemble machine learning (EM...
详细信息
Global warming and population growth have significantly intensified the challenges in securing drinking water supplies. This study investigates transient instabilities of streamflow using ensemble machine learning (EML) and machine learning (ML) methodologies on the South Platte river in the United States. The United States Geological Survey's online database was utilized to obtain the primary dataset. Several technical approaches were employed for preprocessing the initial dataset: cleaning outlier data, clean missing data, and 10 fold cross-validation. nonlinear programming, genetic algorithms, least squares, linear programming, gradient descent, particle swarm optimization, Nelder Mead, and simulated annealing were employed algorithms to develop eightweighted EML models. The results showed that the ensemble learning approach and the aggregation of weak learners by mentioned algorithms have been significantly successful. Particularly, the nonlinear programmingEML (NLP-EML) outperformed others, achieving the highest prediction accuracy with an R2 coefficient equal to 0.97. The probability density function showed that NLP-EML was the most reliable model. Overall, the findings highlight the superior performance and reliability of EML approaches in hydrological modeling, offering practical guidance to experts on the creation of robust ensemble models for improved prediction accuracy.
暂无评论