We consider quasi-variational problems (variational problems having constraint sets depending on their own solutions) which appear in concrete economic models such as social and economic networks, financial derivative models, transportation network congestion and traffic equilibrium. First,...

In this paper, a novel, simple yet efficient method is proposed to approximately solve linear ordinary differential equations (ODEs). Emphasis is put on second-order linear ODEs with variable coefficients. First, the ODE to be solved is transformed to either a Volterra integral equation or a...

The purpose of this paper is to estimate the approximate solutions for variational inequalities. In terms of estimate functions, we establish some estimates of the sizes of the approximate solutions from outside and inside respectively. By considering the behaviors of estimate functions, we give...

In this paper, we introduce the concept of approximate solutions for set-valued mappings and provide a sufficient condition for the existence of approximate solutions of set-valued mappings. We obtain an approximate variational principle for set-valued mappings. Copyright Springer-Verlag Berlin...

In this paper, we introduce the concept of approximate solutions for set-valued mappings and provide a sufficient condition for the existence of approximate solutions of set-valued mappings. We obtain an approximate variational principle for set-valued mappings. Copyright Springer-Verlag Berlin...

We propose a new relationship between the slip and waiting time of real earthquake series. We calculated the Hurst exponents for both time series of slip and waiting time of earthquake sequence in Taiwan CWB (Central Weather Bureau) catalogue. Our findings suggest a good correlation with a...

In general the infimal value of a mathematical program with variational inequality constraints (MPVI) is not stable under perturbations in the sense that the sequence of infimal values for the perturbed programs may not converge to the infimal value of the original problem even in presence of...

The purpose of this paper is to estimate the approximate solutions for variational inequalities. In terms of estimate functions, we establish some estimates of the sizes of the approximate solutions from outside and inside respectively. By considering the behaviors of estimate functions, we give...

Optimization is an important fields of study in science where researchers seek to make the best and most practical decisions. Solving real optimization problems is an intractable issue which calls for generating an approximate using meta-heuristic algorithms. This study proposes a meta-heuristic...

Optimization, which, by definition, can help one find the best solution from all feasible solutions, has sometimes been an interesting and important area for research in science. Solving real and hard optimization problems calls for developing approximate, heuristic, and meta-heuristic...