Multi-objective evolutionary algorithms (MOEAs) are well-suited for solving several complex multi-objective problems with two or three objectives. However, as the number of conflicting objectives increases, the performance of most MOEAs is severely deteriorated. How to improve MOEAs’...

In this paper, we consider a least square semidefinite programming problem under ellipsoidal data uncertainty. We show that the robustification of this uncertain problem can be reformulated as a semidefinite linear programming problem with an additional second-order cone constraint. We then...

A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. First, a suitable scalarization technique is employed for the multi-objective optimal control problem. Then by using a grid of scalarization parameter...

Based on the NEWUOA algorithm, a new derivative-free algorithm is developed, named LCOBYQA. The main aim of the algorithm is to find a minimizer <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$x^{*} \in\mathbb{R}^{n}$</EquationSource> </InlineEquation> of a non-linear function, whose derivatives are unavailable, subject to linear inequality constraints. The algorithm is...</equationsource></inlineequation>

Copositive programming has become a useful tool in dealing with all sorts of optimisation problems. It has however been shown by Murty and Kabadi (Math. Program. 39(2):117–129, <CitationRef CitationID="CR20">1987</CitationRef>) that the strong membership problem for the copositive cone, that is deciding whether or not a given matrix is...</citationref>

Nemirovski’s analysis (SIAM J. Optim. 15:229–251, <CitationRef CitationID="CR15">2005</CitationRef>) indicates that the extragradient method has the O(1/t) convergence rate for variational inequalities with Lipschitz continuous monotone operators. For the same problems, in the last decades, a class of Fejér monotone projection and...</citationref>

Complex polynomial optimization problems arise from real-life applications including radar code design, MIMO beamforming, and quantum mechanics. In this paper, we study complex polynomial optimization models where the objective function takes one of the following three forms: (1) multilinear;...

A general class of variational models with concave priors is considered for obtaining certain sparse solutions, for which nonsmoothness and non-Lipschitz continuity of the objective functions pose significant challenges from an analytical as well as numerical point of view. For computing a...

This paper deals with optimizing the cost of set up, transportation and inventory of a multi-stage production system in presence of bottleneck. The considered optimization model is a mixed integer nonlinear program. We propose two methods based on DC (Difference of Convex) programming and DCA...

In this paper, we present a primal-dual interior-point method for solving nonlinear programming problems. It employs a Levenberg-Marquardt (LM) perturbation to the Karush-Kuhn-Tucker (KKT) matrix to handle indefinite Hessians and a line search to obtain sufficient descent at each iteration. We...