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Correspondence problems are often modelled as quadratic optimization problems over permutations. Common scalable methods for approximating solutions of these NP-hard problems are the spectral relaxation for non-convex energies and the…
Many high dimensional sparse learning problems are formulated as nonconvex optimization. A popular approach to solve these nonconvex optimization problems is through convex relaxations such as linear and semidefinite programming. In this…
Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work…
This paper considers the problem of minimizing a convex expectation function over a closed convex set, coupled with a set of inequality convex expectation constraints. We present a new stochastic approximation type algorithm, namely the…
In this paper, we propose a framework based on the Retrospective Approximation (RA) paradigm to solve optimization problems with a stochastic objective function and general nonlinear deterministic constraints. This framework sequentially…
This paper presents a methodology for using varying sample sizes in sequential quadratic programming (SQP) methods for solving equality constrained stochastic optimization problems. The first part of the paper deals with the delicate issue…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
Given a known matrix that is the sum of a low rank matrix and a masked sparse matrix, we wish to recover both the low rank component and the sparse component. The sparse matrix is masked in the sense that a linear transformation has been…
In this paper, we study a class of fractional semi-infinite polynomial programming problems involving s.o.s-convex polynomial functions. For such a problem, by a conic reformulation proposed in our previous work and the quadratic modules…
We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function. The quantile function is approximated…
Stochastic optimisation problems minimise expectations of random cost functions. We use 'optimise then discretise' method to solve stochastic optimisation. In our approach, accurate quadrature methods are required to calculate the…
We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer…
We investigate the properties of a class of piecewise-fractional maps arising from the introduction of an invariance under rescaling into convex quadratic maps. The subsequent maps are quasiconvex, and pseudoconvex on specific convex cones;…
In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…
This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…
A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added…
This paper is devoted to a new modification of a recently proposed adaptive stochastic mirror descent algorithm for constrained convex optimization problems in the case of several convex functional constraints. Algorithms, standard and its…
We consider the problem of optimal sparse output feedback controller synthesis for continuous linear time invariant systems when the feedback gain is static and subject to specified structural constraints. Introducing an additional term…