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Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
We study model-free learning methods for the output-feedback Linear Quadratic (LQ) control problem in finite-horizon subject to subspace constraints on the control policy. Subspace constraints naturally arise in the field of distributed…
Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization…
The quest for real-time dynamic optimization solutions in the process industry represents a formidable computational challenge, particularly within the realm of applications like model-predictive control, where rapid and reliable…
Advances in quantum algorithms suggest a tentative scaling advantage on certain combinatorial optimization problems. Recent work, however, has also reinforced the idea that barren plateaus render variational algorithms ineffective on large…
In finance, assessing the creditworthiness of loan applicants requires lenders to cluster borrowers using rating scales. Financial institutions must define the scales in compliance with strict institutional constraints, resulting in solving…
This manuscript develops a new framework to analyze and design iterative optimization algorithms built on the notion of Integral Quadratic Constraints (IQC) from robust control theory. IQCs provide sufficient conditions for the stability of…
This paper concerns the problem of learning control policies for an unknown linear dynamical system to minimize a quadratic cost function. We present a method, based on convex optimization, that accomplishes this task robustly: i.e., we…
In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The…
The prospect of quantum solutions for complicated optimization problems is contingent on mapping the original problem onto a tractable quantum energy landscape, e.g. an Ising-type Hamiltonian. Subsequently, techniques like adiabatic…
In this paper we propose a new computational method for designing optimal regulators for high-dimensional nonlinear systems. The proposed approach leverages physics-informed machine learning to solve high-dimensional Hamilton-Jacobi-Bellman…
In this paper, we study the computational complexity of the quadratic unconstrained binary optimization (QUBO) problem under the functional problem FP^NP categorization. We focus on four sub-classes: (1) When all coefficients are integers…
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…
In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…
A challenge for scalability of demand-responsive, elastic optical Dense Wavelength Division Multiplexing (DWDM) and Flexgrid networks is the computational complexity of allocating many optical routes on large networks. We demonstrate that…
A tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max $k$-cut problem is a fundamental combinatorial optimization problem with…
This paper is concerned with the linear quadratic optimal control of discrete-time time-varying system with terminal state constraint. The main contribution is to propose a Q-learning algorithm for the optimal controller when the…
We introduce the quadratic balanced optimization problem (QBOP) which can be used to model equitable distribution of resources with pairwise interaction. QBOP is strongly NP-hard even if the family of feasible solutions has a very simple…
In this work we investigate the min-max-min robust optimization problem and the k-adaptability robust optimization problem for binary problems with uncertain costs. The idea of the first approach is to calculate a set of k feasible…