Related papers: Polynomial Time Algorithms and Extended Formulatio…
We propose a novel global solution algorithm for the network-constrained unit commitment problem incorporating a nonlinear alternating current model of the transmission network, which is a nonconvex mixed-integer nonlinear programming…
We propose three novel mathematical optimization formulations that solve the same two-type heterogeneous multiprocessor scheduling problem for a real-time taskset with hard constraints. Our formulations are based on a global scheduling…
Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
We study the shared processor scheduling problem with a single shared processor where a unit time saving (weight) obtained by processing a job on the shared processor depends on the job. A polynomial-time optimization algorithm has been…
We present a novel algorithm that efficiently computes near-optimal deterministic policies for constrained reinforcement learning (CRL) problems. Our approach combines three key ideas: (1) value-demand augmentation, (2) action-space…
The conventional approach to solving the unit commitment problem involves discrete intervals at an hourly scale, particularly when integrating frequency dynamics to formulate a frequency-constrained unit commitment. To overcome this…
We study the problem of policy synthesis for uncertain partially observable Markov decision processes (uPOMDPs). The transition probability function of uPOMDPs is only known to belong to a so-called uncertainty set, for instance in the form…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…
This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory…
In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
We study the adaptive control of an unknown linear system with a quadratic cost function subject to safety constraints on both the states and actions. The challenges of this problem arise from the tension among safety, exploration,…
The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higher-dimensional polyhedron has recently received increasing attention. In this paper (written for the…
We propose a new second-order method for geodesically convex optimization on the natural hyperbolic metric over positive definite matrices. We apply it to solve the operator scaling problem in time polynomial in the input size and…
The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically…
Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real…
This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
We consider the quadratic optimization problem $\max_{x \in C}\ x^T Q x + q^T x$, where $C\subseteq\mathbb{R}^n$ is a box and $r := \mathrm{rank}(Q)$ is assumed to be $\mathcal{O}(1)$ (i.e., fixed). We show that this case can be solved in…