‎In this paper‎, ‎first we study the weak and strong convergence of solutions to the‎ ‎following first order nonhomogeneous gradient system‎ ‎$$begin{cases}-x'(t)=nablaphi(x(t))+f(t), text{a.e. on} (0,infty)\‎‎x(0)=x_0in Hend{cases}$$ to a critical point of $phi$‎, ‎where‎ ‎$phi$ is a $C^1$ quasi-convex function on a real Hilbert space‎ ‎$H$ with ${rm Argmin}phineqvarnothing$ and $fin L^1(0...

Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient combinatorial algorithms, but whose non-linear convex counterpart is harder and admit significantly less efficient algorithms. This motivates the computation...

in this paper, we conduct a comparative study between the homotopy perturbation method (hpm) and adomian’s decomposition method (adm) for analytic treatment of nonlinear volterra integral equations, and we show that the hpm with a specific convex homotopy is equivalent to the adm for these type of equations.

This paper presents a stochastic nonlinear model predictive control technique for discrete-time uncertain nonlinear systems with particular focus on the batch polymerization reactor application. We consider a nonlinear dynamical system subject to chance constraints (i.e. need to be satisfied probabilistically up to a pre-assigned level). This formulation leads to a finite-horizon chance-constra...

A new method for the efficient solution of free material optimization problems is introduced. The method extends the sequential convex programming (SCP) concept to a class of optimization problems with matrix variables. The basic idea of the new method is to approximate the original optimization problem by a sequence of sub-problems, in which nonlinear functions (defined in matrix variables) ar...

Nonlinear convex optimization has provided both an insightful modeling language and a powerful solution tool to the analysis and design of communication systems over the last decade. A main challenge today is on nonconvex problems in these applications. This chapter presents an overview on some of the important nonconvex optimization problems in communication networks. Four typical applications...

In the field of nonlinear programming (in continuous variables) convex analysis [22, 23] plays a pivotal role both in theory and in practice. An analogous theory for discrete optimization (nonlinear integer programming), called " discrete convex analysis " [18, 17], is developed for L-convex and M-convex functions by adapting the ideas in convex analysis and generalizing the results in matroid ...

This note presents the characterization of the stability set of the first kind for multiobjective nonlinear programming (MONLP) problems with fuzzy parameters either in the constraints or in the objective functions without any differentiability assumptions. These fuzzy parameters are characterized by triangular fuzzy numbers (TFNs). The existing results concerning the parametric space in convex...

In this paper we consider a financial market model with frictions which include transaction costs, bid-ask spread and taxes. By using optimization, linear and nonlinear programming and convex programming techniques, several necessary and sufficient conditions are derived for the weak no-arbitrage. Some results on state prices are also provided. The results of this paper can provide at least som...

In this paper a new model predictive control (MPC) strategy, applicable to a set of nonlinear systems, is proposed and the use of it is demonstrated on a model of a waste treatment reactor. The MPC strategy is an extension of earlier work in optimization-based control [2]. The motivation for the study is to search for approaches to nonlinear MPC without having to solve the full nonlinear proble...