The entropic value-at-risk (EVaR) is a new coherent risk measure, which is an upper bound for both the value-at-risk (VaR) and conditional value-at-risk (CVaR). As important properties, the EVaR is strongly monotone over its domain and strictly monotone over a broad sub-domain including all continuous distributions, while well-known monotone risk measures, such as VaR and … Read more
In this paper, we consider smooth convex optimization problems with simple constraints and inexactness in the oracle information such as value, partial or directional derivatives of the objective function. We introduce a unifying framework, which allows to construct different types of accelerated randomized methods for such problems and to prove convergence rate theorems for them. … Read more
The well-known Jahn-Graef-Younes algorithm, proposed by Jahn in 2006, generates all minimal elements of a finite set with respect to an ordering cone. It consists of two Graef-Younes procedures, namely the forward iteration, which eliminates a part of the non-minimal elements, followed by the backward iteration, which is applied to the reduced set generated by … Read more
In this paper we study necessary optimality conditions for the optimization problem $$\textrm{infimum}f_0(x) \quad \textrm{ subject to } \quad x \in S,$$ where $f_0 \colon \mathbb{R}^n \rightarrow \mathbb{R}$ is a polynomial function and $S \subset \mathbb{R}^n$ is a set defined by polynomial inequalities. Assume that the problem is bounded below and has the Mangasarian–Fromovitz property … Read more
We introduce two new weaker Constraint Qualifications (CQs) for Mathematical Programs with Equilibrium (or Complementarity) Constraints, MPEC for short. One of them is a tailored version of the Constant Rank of Subspace Component (CRSC) and the other is a relaxed version of the MPEC-No Nonzero Abnormal Multiplier Constraint Qualification (MPEC-NNAMCQ). Both incorporate the exact set … Read more
In this paper, we propose a vector transport-free stochastic variance reduced gradient (SVRG) method with general retraction for empirical risk minimization over Riemannian manifold. Existing SVRG methods on manifold usually consider a specific retraction operation, and involve additional computational costs such as parallel transport or vector transport. The vector transport-free SVRG with general retraction we … Read more
In this paper, we propose an inexact Newton-like conditional gradient method for solving constrained systems of nonlinear equations. The local convergence of the new method as well as results on its rate are established by using a general majorant condition. Two applications of such condition are provided: one is for functions whose the derivative satisfies … Read more
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second- and third-order criticality and its evaluation complexity is analyzed as a function of the choice (among existing methods) of an inner algorithm for solving subproblems in … Read more
PSIFA -Pattern Search and Implicit Filtering Algorithm- is a derivative-free algorithm that has been designed for linearly constrained problems with noise in the objective function. It combines some elements of the pattern search approach of Lewis and Torczon (2000) with ideas from the method of implicit filtering of Kelley (2011) enhanced with a further analysis … Read more
We propose a new family of relaxation schemes for mathematical program with complementarity constraints that extends the relaxations of Kadrani, Dussault, Bechakroun from 2009 and the one of Kanzow \& Schwartz from 2011. We discuss the properties of the sequence of relaxed non-linear program as well as stationarity properties of limiting points. A sub-family of … Read more