Neural networks, surrogate models and black box algorithms: theory and applications

In this Ph. D. Thesis we will analyze some of the most used surrogate models, together with a particular type of line search black box strategy. After introducing these powerful tools, we will present the Canonical Duality Theory, the potentiality it has to improve these tools, and some of their applications. The principal contributes of this Thesis are the reformulation of the Radial Basis Neural Network problem in its canonical dual form in Section 2.2 and the application of the surrogate models and black box algorithms presented in this Thesis on various real world problems reported in Chapter 3

Neural networks, surrogate models and black box algorithms: theory and applications

In this Ph. D. Thesis we will analyze some of the most used surrogate models, together with a particular type of line search black box strategy. After introducing these powerful tools, we will present the Canonical Duality Theory, the potentiality it has to improve these tools, and some of their applications. The principal contributes of this Thesis are the reformulation of the Radial Basis Neural Network problem in its canonical dual form in Section 2.2 and the application of the surrogate models and black box algorithms presented in this Thesis on various real world problems reported in Chapter 3

Canonical duality for solving general nonconvex constrained problems

This paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework to cover Lagrange multiplier method and KKT theory. It is proved that if both target function and constraints possess certain patterns necessary for modeling real systems, a perfect dual problem (without duality gap) can be obtained in a unified form with global optimality conditions provided.While the popular augmented Lagrangian method may produce more difficult nonconvex problems due to the nonlinearity of constraints. Some fundamental concepts such as the objectivity and Lagrangian in nonlinear programming are addressed

Global optimal trajectory in Chaos and NP-Hardness

This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory. © 2016 World Scientific Publishing Company

HUBUNGAN DUKUNGAN KELUARGA DENGAN HARGA DIRI PADA PASIEN GAGAL GINJAL KRONIK YANG MENJALANI HEMODIALISA LEBIH DARI ENAM BULAN DI RUMKIT TK II DR. SOEPRAOEN MALANG

Chronic kidney failure is a disorder of renal function in which the body fails to maintain metabolism, fluid and electrolyte balance, thus requiring continuous hemodialis therapy. This study aimed to investigate the correlation between family support and the self-esteem of chronic kidney failure patients who have been undergoing hemodialysis in the Hospital of Soepraoen Malang for over six months. Method : This study usesd a Cross-sectional approach with the independent variable of family suppor and the dependent variable of the self-esteem of chronic kidney failure patients. Purposive sampling was used to determine 34 research samples, who were the kidney failure patients who have been undergoing hemodialysis for over 6 months. The method of data analysis was Spearman correlation. Result : Analysis on the relationship between family support and the self-esteem of kidney failure patients demonstrated a significant value (p-value) of 0,234. Therefore, it was identified that family support was not significantly correlated to the self-esteem of chronic kidney failure patients who have been undergoing hemodialysis in the Hospital of Soepraoen Malang for over six months. Conclusion : Despite having weak correlation, family support is one of the factors of patients’s self-esteem. The result of this study indicated that there were other factors that are more strongly correlated to the self-esteem of chronic kidney failure patients in the Hospital of Soepraoen Malang such as friends, or other social support system