Related papers: Primal-dual interior-point Methods for Semidefinit…
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…
Interior Point Methods are widely used to solve Linear Programming problems. In this work, we present two primal affine scaling algorithms to achieve faster convergence in solving Linear Programming problems. In the first algorithm, we…
This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
In this paper, we propose two novel non-stationary first-order primal-dual algorithms to solve nonsmooth composite convex optimization problems. Unlike existing primal-dual schemes where the parameters are often fixed, our methods use…
In this paper we consider the problem of distributed nonlinear optimisation of a separable convex cost function over a graph subject to cone constraints. We show how to generalise, using convex analysis, monotone operator theory and…
Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bounds on the variables.…
Recently, a lot of attention has been devoted to finding physically realisable operations that realise as closely as possible certain desired transformations between quantum states, e.g. quantum cloning, teleportation, quantum gates, etc.…
In many applications, solutions of convex optimization problems are updated on-line, as functions of time. In this paper, we consider parametric semidefinite programs, which are linear optimization problems in the semidefinite cone whose…
Recently, saddle point problems have received much attention due to their powerful modeling capability for a lot of problems from diverse domains. Applications of these problems occur in many applied areas, such as robust optimization,…
Most linear algebra kernels in interior point methods for linear programming require the solution of linear systems of equation with the matrix $N = A^TD^{-1}A$ (or $AD^{-1}A^T$), where $A$ denotes the constraint matrix of the linear…
In the field of nonlinear mechanics, many challenging problems (e.g. plasticity, contact, masonry structures, nonlinear membranes) turn out to be expressible as conic programs. In general, such problems are non-smooth in nature (plasticity…
While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…
Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods, but scalability can be an issue. To address this shortcoming, over a decade ago, Burer and Monteiro proposed to solve SDPs with few equality…
We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…
We investigate a class of general combinatorial graph problems, including MAX-CUT and community detection, reformulated as quadratic objectives over nonconvex constraints and solved via the alternating direction method of multipliers…
We present a novel analysis of semidefinite programs (SDPs) with positive duality gaps, i.e. different optimal values in the primal and dual problems. These SDPs are extremely pathological, often unsolvable, and also serve as models of more…
In this paper, we propose an infeasible arc-search interior-point algorithm for solving nonlinear programming problems. Most algorithms based on interior-point methods are categorized as line search, since they compute a next iterate on a…
Current state-of-the-art methods for solving discrete optimization problems are usually restricted to convex settings. In this paper, we propose a general approach based on cutting planes for solving nonlinear, possibly nonconvex, binary…