A neurodynamic approach for a class of pseudoconvex semivectorial bilevel optimization problem

The article proposes an exact approach to find the global solution of a nonconvex semivectorial bilevel optimization problem, where the objective functions at each level are pseudoconvex, and the constraints are quasiconvex. Due to its non-convexity, this problem is challenging, but it attracts more and more interest because of its practical applications. The algorithm is developed based on monotonic optimization combined with a recent neurodynamic approach, where the solution set of the lower-level problem is inner approximated by copolyblocks in outcome space. From that, the upper-level problem is solved using the branch-and-bound method. Finding the bounds is converted to pseudoconvex programming problems, which are solved using the neurodynamic method. The algorithm's convergence is proved, and computational experiments are implemented to demonstrate the accuracy of the proposed approach

A globally convergent neurodynamics optimization model for mathematical programming with equilibrium constraints

summary:This paper introduces a neurodynamics optimization model to compute the solution of mathematical programming with equilibrium constraints (MPEC). A smoothing method based on NPC-function is used to obtain a relaxed optimization problem. The optimal solution of the global optimization problem is estimated using a new neurodynamic system, which, in finite time, is convergent with its equilibrium point. Compared to existing models, the proposed model has a simple structure, with low complexity. The new dynamical system is investigated theoretically, and it is proved that the steady state of the proposed neural network is asymptotic stable and global convergence to the optimal solution of MPEC. Numerical simulations of several examples of MPEC are presented, all of which confirm the agreement between the theoretical and numerical aspects of the problem and show the effectiveness of the proposed model. Moreover, an application to resource allocation problem shows that the new method is a simple, but efficient, and practical algorithm for the solution of real-world MPEC problems

A neurodynamic optimization approach to constrained pseudoconvex optimization.

Guo, Zhishan.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (p. 71-82).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement i --- p.iiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Constrained Pseudoconvex Optimization --- p.1Chapter 1.2 --- Recurrent Neural Networks --- p.4Chapter 1.3 --- Thesis Organization --- p.7Chapter 2 --- Literature Review --- p.8Chapter 2.1 --- Pseudo convex Optimization --- p.8Chapter 2.2 --- Recurrent Neural Networks --- p.10Chapter 3 --- Model Description and Convergence Analysis --- p.17Chapter 3.1 --- Model Descriptions --- p.18Chapter 3.2 --- Global Convergence --- p.20Chapter 4 --- Numerical Examples --- p.27Chapter 4.1 --- Gaussian Optimization --- p.28Chapter 4.2 --- Quadratic Fractional Programming --- p.36Chapter 4.3 --- Nonlinear Convex Programming --- p.39Chapter 5 --- Real-time Data Reconciliation --- p.42Chapter 5.1 --- Introduction --- p.42Chapter 5.2 --- Theoretical Analysis and Performance Measurement --- p.44Chapter 5.3 --- Examples --- p.45Chapter 6 --- Real-time Portfolio Optimization --- p.53Chapter 6.1 --- Introduction --- p.53Chapter 6.2 --- Model Description --- p.54Chapter 6.3 --- Theoretical Analysis --- p.56Chapter 6.4 --- Illustrative Examples --- p.58Chapter 7 --- Conclusions and Future Works --- p.67Chapter 7.1 --- Concluding Remarks --- p.67Chapter 7.2 --- Future Works --- p.68Chapter A --- Publication List --- p.69Bibliography --- p.7

Active Sensing of Robot Arms Based on Zeroing Neural Networks: A Biological-Heuristic Optimization Model

Conventional biological-heuristic solutions via zeroing neural network (ZNN) models have achieved preliminary efficiency on time-dependent nonlinear optimization problems handling. However, the investigation on finding a feasible ZNN model to solve the time-dependent nonlinear optimization problems with both inequality and equality constraints still remains stagnant because of the nonlinearity and complexity. To make new progresses on the ZNN for time-dependent nonlinear optimization problems solving, this paper proposes a biological-heuristic optimization model, i.e., inequality and equality constrained optimization ZNN (IECO-ZNN). Such a proposed IECO-ZNN breaks the conditionality that the solutions via ZNN for solving nonlinear optimization problems can not consider the inequality and equality constraints at the same time. The time-dependent nonlinear optimization problem subject to inequality and equality constraints is skillfully converted to a time-dependent equality system by exploiting the Lagrange multiplier rule. The design process for the IECO-ZNN model is presented together with its new architecture illustrated in details. In addition, the conversion equivalence, global stability as well as exponential convergence property are theoretically proven. Moreover, numerical studies, real-world applications to robot arm active sensing, and comparisons sufficiently verify the effectiveness and superiority of the proposed IECO-ZNN model for the time-dependent nonlinear optimization with inequality and equality constraints

A Framework for Controllable Pareto Front Learning with Completed Scalarization Functions and its Applications

Pareto Front Learning (PFL) was recently introduced as an efficient method for approximating the entire Pareto front, the set of all optimal solutions to a Multi-Objective Optimization (MOO) problem. In the previous work, the mapping between a preference vector and a Pareto optimal solution is still ambiguous, rendering its results. This study demonstrates the convergence and completion aspects of solving MOO with pseudoconvex scalarization functions and combines them into Hypernetwork in order to offer a comprehensive framework for PFL, called Controllable Pareto Front Learning. Extensive experiments demonstrate that our approach is highly accurate and significantly less computationally expensive than prior methods in term of inference time.Comment: Under Review at Neural Networks Journa

Optimization techniques in respiratory control system models

One of the most complex physiological systems whose modeling is still an open study is the respiratory control system where different models have been proposed based on the criterion of minimizing the work of breathing (WOB). The aim of this study is twofold: to compare two known models of the respiratory control system which set the breathing pattern based on quantifying the respiratory work; and to assess the influence of using direct-search or evolutionary optimization algorithms on adjustment of model parameters. This study was carried out using experimental data from a group of healthy volunteers under CO2 incremental inhalation, which were used to adjust the model parameters and to evaluate how much the equations of WOB follow a real breathing pattern. This breathing pattern was characterized by the following variables: tidal volume, inspiratory and expiratory time duration and total minute ventilation. Different optimization algorithms were considered to determine the most appropriate model from physiological viewpoint. Algorithms were used for a double optimization: firstly, to minimize the WOB and secondly to adjust model parameters. The performance of optimization algorithms was also evaluated in terms of convergence rate, solution accuracy and precision. Results showed strong differences in the performance of optimization algorithms according to constraints and topological features of the function to be optimized. In breathing pattern optimization, the sequential quadratic programming technique (SQP) showed the best performance and convergence speed when respiratory work was low. In addition, SQP allowed to implement multiple non-linear constraints through mathematical expressions in the easiest way. Regarding parameter adjustment of the model to experimental data, the evolutionary strategy with covariance matrix and adaptation (CMA-ES) provided the best quality solutions with fast convergence and the best accuracy and precision in both models. CMAES reached the best adjustment because of its good performance on noise and multi-peaked fitness functions. Although one of the studied models has been much more commonly used to simulate respiratory response to CO2 inhalation, results showed that an alternative model has a more appropriate cost function to minimize WOB from a physiological viewpoint according to experimental data.Postprint (author's final draft

Data-Driven Control of Unknown Systems: A Linear Programming Approach

We consider the problem of discounted optimal state-feedback regulation for general unknown deterministic discrete-time systems. It is well known that open-loop instability of systems, non-quadratic cost functions and complex nonlinear dynamics, as well as the on-policy behavior of many reinforcement learning (RL) algorithms, make the design of model-free optimal adaptive controllers a challenging task. We depart from commonly used least-squares and neural network approximation methods in conventional model-free control theory, and propose a novel family of data-driven optimization algorithms based on linear programming, off-policy Q-learning and randomized experience replay. We develop both policy iteration (PI) and value iteration (VI) methods to compute an approximate optimal feedback controller with high precision and without the knowledge of a system model and stage cost function. Simulation studies confirm the effectiveness of the proposed methods