‎In this paper‎, ‎we present an algorithm for generating approximate nondominated points of a multiobjective optimization problem (MOP)‎, ‎where the constraints and the objective functions are convex‎. ‎We provide outer and inner approximations of nondominated points and prove that inner approximations provide a set of approximate weakly nondominated points‎. ‎The proposed algorithm can be appl...

in this paper, we describe our implementation of an interior point algorithm for large scale systems. first we identify system with small and medium methods convex optimization, then we use interior point method for identification. finally we offer an interior point method that uses nonlinear cost function and see that we achieve a good trade-off between error and cpu time. actually, in this pa...

Convex optimization is a special class of optimization problems, that includes many problems of interest such as least squares and linear programming problems. Convex optimization problems are considered especially important because several efficient algorithms exist for solving them; as a result, many machine learning problems have been modeled as convex optimization. In a typical convex optim...

the problem of finding the minimum cost multi-commodity flow in an undirected and completenetwork is studied when the link costs are piecewise linear and convex. the arc-path model and overflowmodel are presented to formulate the problem. the results suggest that the new overflow model outperformsthe classical arc-path model for this problem. the classical revised simplex, frank and wolf and a ...

Abstract In this paper we consider a problem, called convex projection, of projecting set onto subspace. We will show that to projection one can assign particular multi-objective optimization such the solution problem also solves (and vice versa), which is analogous result in polyhedral case considered Löhne and Weißing (Math Methods Oper Res 84(2):411–426, 2016). practice, however, only comput...

We investigate a fast optimization method for determining the minimizer of the negative Poisson likelihood function for the global analysis of fluorescence lifetime microscopy. Using the alternating optimization strategy, we iteratively solve a non-convex optimization problem to estimate the lifetime parameters and a convex optimization problem to estimate the concentration parameters. We effec...

In a convex optimization problem, x ∈ R is a vector known as the optimization variable, f : R → R is a convex function that we want to minimize, and C ⊆ R is a convex set describing the set of feasible solutions. From a computational perspective, convex optimization problems are interesting in the sense that any locally optimal solution will always be guaranteed to be globally optimal. Over the...

This paper studies robust solutions and semidefinite linear programming (SDP) relaxations of a class of convex polynomial optimization problems in the face of data uncertainty. The class of convex optimization problems, called robust SOS-convex polynomial optimization problems, includes robust quadratically constrained convex optimization problems and robust separable convex polynomial optimiza...

In this paper we consider a fractional optimization problem that minimizes the ratio of two quadratic functions subject to a strictly convex quadratic constraint. First using the extension of Charnes-Cooper transformation, an equivalent homogenized quadratic reformulation of the problem is given. Then we show that under certain assumptions, it can be solved to global optimality using semidefini...