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Efficient algorithms for convex optimization, such as the ellipsoid method, require an a priori bound on the radius of a ball around the origin guaranteed to contain an optimal solution if one exists. For linear and convex quadratic…
A general problem in optimal control consists of finding a terminal reward that makes the value function independent of the horizon. Such a terminal reward can be interpreted as a max-plus eigenvector of the associated Lax-Oleinik…
Global polynomial optimization methods typically rely on compactness of the feasible region in order to find solutions. These methods can incur considerable computational expense and most commercially available solvers do not verify the…
We consider optimal stopping problems, in which a sequence of independent random variables is drawn from a known continuous density. The objective of such problems is to find a procedure which maximizes the expected reward; this is often…
We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights, i.e., optimal multiple stopping, for a robust evaluation that accounts for model…
In this paper, we give a quadratic Goldreich-Levin algorithm that is close to optimal in the following ways. Given a bounded function $f$ on the Boolean hypercube $\mathbb{F}_2^n$ and any $\varepsilon>0$, the algorithm returns a quadratic…
The famous least squares Monte Carlo (LSM) algorithm combines linear least square regression with Monte Carlo simulation to approximately solve problems in stochastic optimal stopping theory. In this work, we propose a quantum LSM based on…
In this paper we consider the following optimal stopping problem $$V^{\omega}_{\rm A}(s) = \sup_{\tau\in\mathcal{T}} \mathbb{E}_{s}[e^{-\int_0^\tau \omega(S_w) dw} g(S_\tau)],$$ where the process $S_t$ is a jump-diffusion process,…
We present a solution to an optimal stopping problem for a process with a wide-class of novel dynamics. The dynamics model the support/resistance line concept from financial technical analysis.
This paper shows the usefulness of the Perov contraction theorem, which is a generalization of the classical Banach contraction theorem, for solving Markov dynamic programming problems. When the reward function is unbounded, combining an…
In this paper we consider discrete time stochastic optimal control problems over infinite and finite time horizons. We show that for a large class of such problems the Taylor polynomials of the solutions to the associated Dynamic…
We revisit the classical singular control problem of minimizing running and controlling costs. The problem arises in inventory control, as well as in healthcare management and mathematical finance. Existing studies have shown the optimality…
We consider a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a…
We give a fully polynomial randomized approximation scheme to compute a lower bound for the matching polynomial of any weighted graph at a positive argument. For the matching polynomial of complete bipartite graphs with bounded weights…
In this paper, we establish an exponential periodic turnpike property for linear quadratic optimal control problems governed by periodic systems in infinite dimension. We show that the optimal trajectory converges exponentially to a…
We consider min-max optimization problems for polynomial functions, where a multivariate polynomial is maximized with respect to a subset of variables, and the resulting maximal value is minimized with respect to the remaining variables.…
This paper is concerned with the solution of the optimal stopping problem associated to the valuation of Perpetual American options driven by continuous time Markov chains. We introduce a new dynamic approach for the numerical pricing of…
This paper presents a canonical dual approach for solving a nonconvex global optimization problem governed by a sum of fourth-order polynomial and a log-sum-exp function. Such a problem arises extensively in engineering and sciences. Based…
This work presents an algorithmic scheme for solving the infinite-time constrained linear quadratic regulation problem. We employ an accelerated version of a popular proximal gradient scheme, commonly known as the Forward-Backward Splitting…
In this paper, we investigate the problem of finding tight linear lower bounding functions for multivariate polynomials over boxes. These functions are obtained by the expansion of polynomials into Bernstein form and using the linear least…