Related papers: An Efficient Solution Method for Solving Convex Se…
We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) relaxation to compute strong lower bounds and generate…
Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employed by practitioners for their implementability and…
The aim of this manuscript is to approach by means of first order differential equations/inclusions convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the…
We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…
This paper introduces a new method for solving quadratic programs using primal-dual interior-point methods. Instead of handling complementarity as an explicit equation in the Karush-Kuhn-Tucker (KKT) conditions, we ensure that…
In this paper, we analyze in depth a simplicial decomposition like algorithmic framework for large scale convex quadratic programming. In particular, we first propose two tailored strategies for handling the master problem. Then, we…
In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those…
A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function. The algorithmic…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
Convex quadratic programming (QP) is an important class of optimization problem with wide applications in practice. The classic QP solvers are based on either simplex or barrier method, both of which suffer from the scalability issue…
Sparse inverse covariance selection is a fundamental problem for analyzing dependencies in high dimensional data. However, such a problem is difficult to solve since it is NP-hard. Existing solutions are primarily based on convex…
Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity…
This paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework to cover Lagrange multiplier method and KKT theory. It is proved that if both target function and…
Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…
The article is devoted to the development of algorithmic methods ensuring efficient complexity bounds for strongly convex-concave saddle point problems in the case when one of the groups of variables is high-dimensional, and the other is…
In this article, we use the monotonic optimization approach to propose an outcome-space outer approximation by copolyblocks for solving strictly quasiconvex multiobjective programming problems and especially in the case that the objective…
In this paper, we present an interior point algorithm with a full-Newton step for solving a linearly constrained convex optimization problem, in which we propose a generalization of the work of Kheirfam and Nasrollahi…
This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive…
In this paper, we propose the Bi-Sub-Gradient (Bi-SG) method, which is a generalization of the classical sub-gradient method to the setting of convex bi-level optimization problems. This is a first-order method that is very easy to…
In this paper we present an efficient active-set method for the solution of convex quadratic programming problems with general piecewise-linear terms in the objective, with applications to sparse approximations and risk-minimization. The…