In recent years, optimization theory has been greatly impacted by the advent of sum of squares (SOS) optimization. The reliance of this technique on large-scale semidefinite programs however, has limited the scale of problems to which it can be applied. In this paper, we introduce DSOS and SDSOS optimization as linear programming and second-order cone … Read more
In this note an erratum is provided to the article “On the DJL conjecture for order 6” by Naomi Shaked-Monderer, published in Operators and Matrices 11(1), 2017, 71–88. We will demonstrate and correct two errors in this article. The first error is in the statement of a proposition, which omits a certain category of extreme … Read more
The general formulation for finding the L1-norm best-fit subspace for a point set in $m$-dimensions is a nonlinear, nonconvex, nonsmooth optimization problem. In this paper we present a procedure to estimate the L1-norm best-fit one-dimensional subspace (a line through the origin) to data in $\Re^m$ based on an optimization criterion involving linear programming but which … Read more
This paper studies the vehicle routing problem with time windows and multiple deliverymen in which customer demands are uncertain and belong to a predetermined polytope. In addition to the routing decisions, this problem aims to define the number of deliverymen used to provide the service to the customers on each route. A new mathematical formulation … Read more
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are amenable to exact copositive programming reformulations of polynomial size. These convex optimization problems are NP-hard but admit a conservative semidefinite programming … Read more
In this paper we extend naturally the scalarization proximal point method to solve multiobjective unconstrained minimization problems, proposed by Apolinario et al.(2016), from Euclidean spaces to Hadamard manifolds for locally Lipschitz and quasiconvex vector objective functions. Moreover, we present a convergence analysis, under some mild assumptions on the multiobjective function, for two inexact variants of … Read more
Designing distributed algorithms for empirical risk minimization (ERM) has become an active research topic in recent years because of the practical need to deal with the huge volume of data. In this paper, we propose a general framework for training an ERM model via solving its dual problem in parallel over multiple machines. Our method … Read more
We give explicit solutions for utility optimization problems in the presence of Knightian uncertainty in continuous time with nondominated priors and finite time horizon in a diffusion model. We assume that the uncertainty set is compact and time dependent on $[0,T]$. We solve the robust optimization problem explicitly both when the investor’s utility is of … Read more
The alternating direction method of multipliers is a powerful operator splitting technique for solving structured optimization problems. For convex optimization problems, it is well-known that the algorithm generates iterates that converge to a solution, provided that it exists. If a solution does not exist, then the iterates diverge. Nevertheless, we show that they yield conclusive … Read more
We propose piecewise linear kernel-based support vector clustering (SVC) as a new approach tailored to data-driven robust optimization. By solving a quadratic program, the distributional geometry of massive uncertain data can be effectively captured as a compact convex uncertainty set, which considerably reduces conservatism of robust optimization problems. The induced robust counterpart problem retains the … Read more