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This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We consider high dimensional random optimization problems where the dynamical variables are subjected to non-convex excluded volume constraints. We focus on the case in which the cost function is a simple quadratic cost and the excluded…
Optimization is fundamental in many areas of science, from computer science and information theory to engineering and statistical physics, as well as to biology or social sciences. It typically involves a large number of variables and a…
A wide class of problems in combinatorics, computer science and physics can be described along the following lines. There are a large number of variables ranging over a finite domain that interact through constraints that each bind a few…
This paper is concerned with a stochastic linear-quadratic optimal control problem in a finite time horizon, where the coefficients of the control system are allowed to be random, and the weighting matrices in the cost functional are…
We study a simple and exactly solvable model for the generation of random satisfiability problems. These consist of $\gamma N$ random boolean constraints which are to be satisfied simultaneously by $N$ logical variables. In…
We analyze statistical features of the ``optimization landscape'' in a random version of one of the simplest constrained optimization problems of the least-square type: finding the best approximation for the solution of an overcomplete…
In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed…
Symmetric quantum signal processing provides a parameterized representation of a real polynomial, which can be translated into an efficient quantum circuit for performing a wide range of computational tasks on quantum computers. For a given…
We present a fully probabilistic approach for solving binary optimization problems with black-box objective functions and with budget constraints. In the probabilistic approach, the optimization variable is viewed as a random variable and…
Exact free energy minimization is a convex optimization problem that is usually approximated with stochastic sampling methods. Deterministic approximations have been less successful because many desirable properties have been difficult to…
Bayesian variable selection has gained much empirical success recently in a variety of applications when the number $K$ of explanatory variables $(x_1,...,x_K)$ is possibly much larger than the sample size $n$. For generalized linear…
We introduce a general random model of a combinatorial optimization problem with geometric structure that encapsulates both linear programming and integer linear programming. Let $Q$ be a bounded set called the feasible set, $E$ be an…
A general method for deriving closed reduced models of Hamiltonian dynamical systems is developed using techniques from optimization and statistical estimation. As in standard projection operator methods, a set of resolved variables is…
We introduce a new technique to optimize a linear cost function subject to a one-dimensional affine homogeneous quadratic integral inequality, i.e., the requirement that a homogeneous quadratic integral functional, affine in the…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…
Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…
We propose a general algorithm to enumerate all solutions of a zero-dimensional polynomial system with respect to a given cost function. The algorithm is developed and is used to study a polynomial system obtained by discretizing the steady…
Finding the global minimum of a cost function given by the sum of a quadratic and a linear form in N real variables over (N-1)- dimensional sphere is one of the simplest, yet paradigmatic problems in Optimization Theory known as the "trust…
This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems. The main tools are the graphical models and approximate message-passing algorithm together with the cavity…