Singularity theory for nonlinear optimization problems

A Particle Swarm Optimization Algorithm for Mixed-Variable Nonlinear Problems

Many engineering design problems involve a combination of both continuous anddiscrete variables. However, the number of studies scarcely exceeds a few on mixed-variableproblems. In this research Particle Swarm Optimization (PSO) algorithm is employed to solve mixedvariablenonlinear problems. PSO is an efficient method of dealing with nonlinear and non-convexoptimization problems. In this paper,...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

On some problems in singularity theory

Optimization Techniques for Tree-Structured Nonlinear Problems

Robust model predictive control approaches and other applications lead to nonlinear optimization problems defined on (scenario) trees. We present structure-preserving Quasi-Newton update formulas as well as structured inertia correction techniques that allow to solve these problems by interior-point methods with specialized KKT solvers for tree-structured optimization problems. The same type of...

Complexity and algorithms for nonlinear optimization problems

Nonlinear optimization algorithms are rarely discussed from a complexity point of view. Even the concept of solving nonlinear problems on digital computers is not well defined. The focus here is on a complexity approach for designing and analyzing algorithms for nonlinear optimization problems providing optimal solutions with prespecified accuracy in the solution space. We delineate the complex...