16 research outputs found
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
Self-adaptive algorithms for quasiconvex programming and applications to machine learning
For solving a broad class of nonconvex programming problems on an unbounded
constraint set, we provide a self-adaptive step-size strategy that does not
include line-search techniques and establishes the convergence of a generic
approach under mild assumptions. Specifically, the objective function may not
satisfy the convexity condition. Unlike descent line-search algorithms, it does
not need a known Lipschitz constant to figure out how big the first step should
be. The crucial feature of this process is the steady reduction of the step
size until a certain condition is fulfilled. In particular, it can provide a
new gradient projection approach to optimization problems with an unbounded
constrained set. The correctness of the proposed method is verified by
preliminary results from some computational examples. To demonstrate the
effectiveness of the proposed technique for large-scale problems, we apply it
to some experiments on machine learning, such as supervised feature selection,
multi-variable logistic regressions and neural networks for classification
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 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
Robust Linear Neural Network for Constrained Quadratic Optimization
Based on the feature of projection operator under box constraint, by using convex analysis method, this paper proposed three robust linear systems to solve a class of quadratic optimization problems. Utilizing linear matrix inequality (LMI) technique, eigenvalue perturbation theory, Lyapunov-Razumikhin method, and LaSalle’s invariance principle, some stable criteria for the related models are also established. Compared with previous criteria derived in the literature cited herein, the stable criteria established in this paper are less conservative and more practicable. Finally, a numerical simulation example and an application example in compressed sensing problem are also given to illustrate the validity of the criteria established in this paper