Quasiconvex Optimization for Robust Geometric Reconstruction

Explicitly quasiconvex optimization problems

We present some properties of explicitly quasiconvex functions, which play an important role in both multicriteria and scalar optimization. Some of these results were recently obtained together with Ovidiu Bagdasar during a research visit at the University of Derby (UK), within the project

Stability for Properly Quasiconvex Vector Optimization Problem

The aim of this paper is to study the stability aspects of various types of solution set of a vector optimization problem both in the given space and in its image space by perturbing the objective function and the feasible set. The Kuratowski– Painlevé set-convergence of the sets of minimal, weak minimal and Henig proper minimal points of the perturbed problems to the corresponding minimal set ...

Complexity of integer quasiconvex polynomial optimization

We study a particular case of integer polynomial optimization: Minimize a polynomial F̂ on the set of integer points described by an inequality system F1 ≤ 0, . . . , Fs ≤ 0, where F̂ , F1, . . . , Fs are quasiconvex polynomials in n variables with integer coefficients. We design an algorithm solving this problem that belongs to the time-complexity class O(s) · lO(1) · dO(n) · 2O(n 3), where d ≥ ...

Portfolio Optimization with Quasiconvex Risk Measures

The inexact projected gradient method for quasiconvex vector optimization problems

Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the nonnegative octant. Due to its real life applications, it is important to have practical solution approaches for computing. In this work, we consider the inexact projected gradient-like method for solving smooth constra...