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Semidefinite programming (SDP) is a powerful framework from convex optimization that has striking potential for data science applications. This paper develops a provably correct randomized algorithm for solving large, weakly constrained SDP…
This paper formulates a semidefinite programming relaxation for a long horizon direct-torque finite-control-set model predictive control problem. In parallel with this relaxation, a conventional branch-and-bound algorithm tailored for the…
This paper addresses the optimization problem of minimizing non-convex continuous functions, which is relevant in the context of high-dimensional machine learning applications characterized by over-parametrization. We analyze a randomized…
Despite the numerous uses of semidefinite programming (SDP) and its universal solvability via interior point methods (IPMs), it is rarely applied to practical large-scale problems. This mainly owes to the computational cost of IPMs that…
Max-cut, clustering, and many other partitioning problems that are of significant importance to machine learning and other scientific fields are NP-hard, a reality that has motivated researchers to develop a wealth of approximation…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
We consider the problem of optimal input design for estimating uncertain parameters in a discrete-time linear state space model, subject to simultaneous amplitude and l1/l2-norm constraints on the admissible inputs. We formulate this…
The minimum sum-of-squares clustering (MSSC), or k-means type clustering, is traditionally considered an unsupervised learning task. In recent years, the use of background knowledge to improve the cluster quality and promote…
A longstanding problem related to floating-point implementation of numerical programs is to provide efficient yet precise analysis of output errors. We present a framework to compute lower bounds on largest absolute roundoff errors, for a…
We study a budgeted hyper-parameter tuning problem, where we optimize the tuning result under a hard resource constraint. We propose to solve it as a sequential decision making problem, such that we can use the partial training progress of…
For solving large-scale non-convex problems, we propose inexact variants of trust region and adaptive cubic regularization methods, which, to increase efficiency, incorporate various approximations. In particular, in addition to approximate…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
Wideband communication receivers often deal with the problems of detecting weak signals from distant sources received together with strong nearby interferers. When the techniques of random modulation are used in communication system…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
Bounding the correlations predicted by quantum theory is an important challenge in quantum information science. Today's leading approach is semidefinite programming relaxations, but existing methods still cannot account for many relevant…
We present a general approach to rounding semidefinite programming relaxations obtained by the Sum-of-Squares method (Lasserre hierarchy). Our approach is based on using the connection between these relaxations and the Sum-of-Squares proof…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
Unconstrained submodular maximization captures many NP-hard combinatorial optimization problems, including Max-Cut, Max-Di-Cut, and variants of facility location problems. Recently, Buchbinder et al. presented a surprisingly simple linear…
Semidefinite programming is an important tool to tackle several problems in data science and signal processing, including clustering and community detection. However, semidefinite programs are often slow in practice, so speed up techniques…