WITHDRAWN: Nonconvex optimization based on DC programming and DCA in the search of a global optimum of a nonconvex function

Motivated by the successful use of a pseudo-cut strategy within the setting of constrained nonlinear and nonconvex optimization in Lasdon et al. (2010), we propose a framework for general pseudo-cut strategies in global optimization that provides a broader and more comprehensive range of methods. The fundamental idea is to introduce linear cutting planes that provide temporary, possibly invalid, restrictions on the space of feasible solutions, as proposed in the setting of the tabu search metaheuristic in Glover (1989), in order to guide a solution process toward a global optimum, where the cutting planes can be discarded and replaced by others as the process continues. These strategies can be used separately or in combination, and can also be used to supplement other approaches to nonlinear global optimization. Our strategies also provide mechanisms for generating trial solutions that can be used with or without the temporary enforcement of the pseudo-cuts.

Download Full-text

Pseudo-Cut Strategies for Global Optimization

International Journal of Applied Metaheuristic Computing ◽

10.4018/jamc.2011100101 ◽

2011 ◽

Vol 2 (4) ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Fred Glover ◽

Leon Lasdon ◽

John Plummer ◽

Abraham Duarte ◽

Rafael Marti ◽

...

Keyword(s):

Global Optimization ◽

Tabu Search ◽

Nonconvex Optimization ◽

Cutting Planes ◽

Solution Process ◽

Global Optimum ◽

Fundamental Idea ◽

Feasible Solutions

Motivated by the successful use of a pseudo-cut strategy within the setting of constrained nonlinear and nonconvex optimization in Lasdon et al. (2010), we propose a framework for general pseudo-cut strategies in global optimization that provides a broader and more comprehensive range of methods. The fundamental idea is to introduce linear cutting planes that provide temporary, possibly invalid, restrictions on the space of feasible solutions, as proposed in the setting of the tabu search metaheuristic in Glover (1989), in order to guide a solution process toward a global optimum, where the cutting planes can be discarded and replaced by others as the process continues. These strategies can be used separately or in combination, and can also be used to supplement other approaches to nonlinear global optimization. Our strategies also provide mechanisms for generating trial solutions that can be used with or without the temporary enforcement of the pseudo-cuts.

Download Full-text

Genetic search - An approach to the nonconvex optimization problem

10.2514/6.1989-1177 ◽

1989 ◽

Cited By ~ 5

Author(s):

P. HAJELA

Keyword(s):

Nonconvex Optimization ◽

Optimization Problem ◽

Genetic Search

Download Full-text

Opinion Dynamics Optimization by Varying Susceptibility to Persuasion via Non-Convex Local Search

ACM Transactions on Knowledge Discovery from Data ◽

10.1145/3466617 ◽

2021 ◽

Vol 16 (2) ◽

pp. 1-34

Author(s):

Rediet Abebe ◽

T.-H. HUBERT Chan ◽

Jon Kleinberg ◽

Zhibin Liang ◽

David Parkes ◽

...

Keyword(s):

Local Search ◽

Objective Function ◽

Iterative Process ◽

Large Scale ◽

Opinion Dynamics ◽

Theoretical Models ◽

Global Optimum ◽

Local Optimum ◽

Opinion Formation ◽

Long Line

A long line of work in social psychology has studied variations in people’s susceptibility to persuasion—the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people’s intrinsic opinions, it is also natural to consider interventions that modify people’s susceptibility to persuasion. In this work, motivated by this fact, we propose an influence optimization problem. Specifically, we adopt a popular model for social opinion dynamics, where each agent has some fixed innate opinion, and a resistance that measures the importance it places on its innate opinion; agents influence one another’s opinions through an iterative process. Under certain conditions, this iterative process converges to some equilibrium opinion vector. For the unbudgeted variant of the problem, the goal is to modify the resistance of any number of agents (within some given range) such that the sum of the equilibrium opinions is minimized; for the budgeted variant, in addition the algorithm is given upfront a restriction on the number of agents whose resistance may be modified. We prove that the objective function is in general non-convex. Hence, formulating the problem as a convex program as in an early version of this work (Abebe et al., KDD’18) might have potential correctness issues. We instead analyze the structure of the objective function, and show that any local optimum is also a global optimum, which is somehow surprising as the objective function might not be convex. Furthermore, we combine the iterative process and the local search paradigm to design very efficient algorithms that can solve the unbudgeted variant of the problem optimally on large-scale graphs containing millions of nodes. Finally, we propose and evaluate experimentally a family of heuristics for the budgeted variant of the problem.

Download Full-text

Global optimization based on active preference learning with radial basis functions

Machine Learning ◽

10.1007/s10994-020-05935-y ◽

2020 ◽

Author(s):

Alberto Bemporad ◽

Dario Piga

Keyword(s):

Global Optimization ◽

Objective Function ◽

Decision Maker ◽

Optimization Problems ◽

Global Optimum ◽

Bayesian Optimization ◽

Preference Learning ◽

Global Optimizer ◽

Radial Basis ◽

Decision Vector

AbstractThis paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as “this is better than that” between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. A radial-basis function surrogate is fit via linear or quadratic programming, satisfying if possible the preferences expressed by the decision maker on existing samples. The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred. Compared to active preference learning based on Bayesian optimization, we show that our approach is competitive in that, within the same number of comparisons, it usually approaches the global optimum more closely and is computationally lighter. Applications of the proposed algorithm to solve a set of benchmark global optimization problems, for multi-objective optimization, and for optimal tuning of a cost-sensitive neural network classifier for object recognition from images are described in the paper. MATLAB and a Python implementations of the algorithms described in the paper are available at http://cse.lab.imtlucca.it/~bemporad/glis.

Download Full-text

Software-Defined Optimal Computation Task Scheduling in Vehicular Edge Networking

Sensors ◽

10.3390/s21030955 ◽

2021 ◽

Vol 21 (3) ◽

pp. 955

Author(s):

Zhiyuan Li ◽

Ershuai Peng

Keyword(s):

Task Scheduling ◽

Scheduling Algorithm ◽

Dynamic Network ◽

Parameter Tuning ◽

Global Optimum ◽

Research Field ◽

Edge Computing ◽

Transmission Delay ◽

Smart Vehicles ◽

Network Bandwidth

With the development of smart vehicles and various vehicular applications, Vehicular Edge Computing (VEC) paradigm has attracted from academic and industry. Compared with the cloud computing platform, VEC has several new features, such as the higher network bandwidth and the lower transmission delay. Recently, vehicular computation-intensive task offloading has become a new research field for the vehicular edge computing networks. However, dynamic network topology and the bursty computation tasks offloading, which causes to the computation load unbalancing for the VEC networking. To solve this issue, this paper proposed an optimal control-based computing task scheduling algorithm. Then, we introduce software defined networking/OpenFlow framework to build a software-defined vehicular edge networking structure. The proposed algorithm can obtain global optimum results and achieve the load-balancing by the virtue of the global load status information. Besides, the proposed algorithm has strong adaptiveness in dynamic network environments by automatic parameter tuning. Experimental results show that the proposed algorithm can effectively improve the utilization of computation resources and meet the requirements of computation and transmission delay for various vehicular tasks.

Download Full-text