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Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
We study dual-based algorithms for distributed convex optimization problems over networks, where the objective is to minimize a sum $\sum_{i=1}^{m}f_i(z)$ of functions over in a network. We provide complexity bounds for four different…
This paper deals with finding an $n$-dimensional solution $x$ to a system of quadratic equations of the form $y_i=|\langle{a}_i,x\rangle|^2$ for $1\le i \le m$, which is also known as phase retrieval and is NP-hard in general. We put forth…
Quadratic Unconstrained Binary Optimization (QUBO) is recognized as a unifying framework for modeling a wide range of problems. Problems can be solved with commercial solvers customized for solving QUBO and since QUBO have degree two, it is…
We present a fully adaptive multiresolution scheme for spatially one-dimensional quasilinear strongly degenerate parabolic equations with zero-flux and periodic boundary conditions. The numerical scheme is based on a finite volume…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
We present several new results about smoothed analysis of multiobjective optimization problems. Motivated by the discrepancy between worst-case analysis and practical experience, this line of research has gained a lot of attention in the…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
In this paper, we present a review of three widely-used practical square root algorithms. We then describe a unifying framework where each of these well-known algorithms can be seen as a special case of it. The framework with singular…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined components: one-dimensional linear optimization one…
Solving optimisation problems is a promising near-term application of quantum computers. Quantum variational algorithms leverage quantum superposition and entanglement to optimise over exponentially large solution spaces using an…
The sum-of-squares method can give rigorous lower bounds on the energy of quantum Hamiltonians. Unfortunately, typically using this method requires solving a semidefinite program, which can be computationally expensive. Further, the…
Many real world applications can be framed as multi-objective optimization problems, where we wish to simultaneously optimize for multiple criteria. Bayesian optimization techniques for the multi-objective setting are pertinent when the…
The Sum of Square Roots (SSR) problem is the following computational problem: Given positive integers $a_1, \dots, a_k$, and signs $\delta_1, \dots, \delta_k \in \{-1, 1\}$, check if $\sum_{i=1}^k \delta_i \sqrt{a_i} > 0$. The problem is…
We consider two problems that arise in machine learning applications: the problem of recovering a planted sparse vector in a random linear subspace and the problem of decomposing a random low-rank overcomplete 3-tensor. For both problems,…
We study the exact counting problem for all lattice rectangles contained in the square $[0,n)\times[0,n)$, including non-axis-parallel ones. Starting from the standard parametrization by a primitive direction $(u,v)$ and two side lengths,…
In this paper problem of construction of optimal quadrature formulas in $W_2^{(m,m-1)}(0,1)$ space is considered. Here by using Sobolev's algorithm when $m=1,2$ we find the optimal coefficients of the quadrature formulas of the form $$…
We propose and analyze a set of variational quantum algorithms for solving quadratic unconstrained binary optimization problems where a problem consisting of $n_c$ classical variables can be implemented on $\mathcal O(\log n_c)$ number of…
We revisit the convergence analysis of two approximation hierarchies for polynomial optimization on the unit sphere. The first one is based on the moment-sos approach and gives semidefinite bounds for which Fang and Fawzi (2021) showed an…