Open shop scheduling problems (OSSP) are highly significant in engineering and industry, involving critical scheduling challenges. The job type determines the duration required for material transfer between machines and remains unaffected by distance, eliminating any waiting time for transfers....

The presented paper considers the pricing and lot-sizing decisions for a manufacturer who produces and sells a single product in different selling channels i.e physical stock, website, mobile, etc. The objective is to find the production plan and prices of each channel to maximize the total...

We present a novel variational inequality model (VIM) to capture the complex real decision-making process in multi-tiered supply chain networks (MSCN) without strictly limiting the features of related functions. The VIM is formulated with the equilibrium conditions on links as the optimization...

We consider the solution of a recurrent sub–problem within both constrained and unconstrained Nonlinear Programming: namely the minimization of a quadratic function subject to linear constraints. This problem appears in a number of LBM frameworks, and to some extent it reveals a close analogy...

Solving non-linear parabolic partial differential equations (PDEs) in high dimension becomes an interest for its curse of dimensionality problem. Recently, a deep learning method associated with a backward stochastic differential equation (deep-BSDE) to solve the PDEs draws intensive discussions...

Portfolio optimization is an activity for balancing return and risk. In this paper, we used mean-variance (M-V) portfolio models with buy-in threshold and cardinality constraints. This model can be formulated as a mixed integer nonlinear programming (MINLP) problem. To solve this constrained...

Chapter 1 Nonlinear Programming -- Chapter 2 Perron-Frobenius Theorem -- Chapter 3 Dominant Diagonal Matrix and Quadratic Form -- Chapter 4 Recent Issue on Eigenvalue Problem -- Appendix Lists of Mathematical Theorems and Definitions.

Preliminaries -- C Representing Functionals -- Application in Nonlinear Optimization -- Application in Vector Optimization -- Application in Set Optimization -- Basics of Deep Learning -- Deep Learning with Set-Valued Inputs.

Neural networks offer a promising tool for the analysis of nonlinear economies. In this paper, we derive conditions for the global stability of nonlinear rational expectations equilibria under neural network learning. We demonstrate the applicability of the conditions in analytical and numerical...