Related papers: Success probability of the $L_0$-regularized box-c…
In this paper, the problem of finding optimal success probabilities of static linear optics quantum gates is linked to the theory of convex optimization. It is shown that by exploiting this link, upper bounds for the success probability of…
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…
It is well-known that the Burer-Monteiro (B-M) factorization approach can efficiently solve low-rank matrix optimization problems under the RIP condition. It is natural to ask whether B-M factorization-based methods can succeed on any…
Multi-objective Bayesian optimization has been widely adopted in scientific experiment design, including drug discovery and hyperparameter optimization. In practice, regulatory or safety concerns often impose additional thresholds on…
We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by…
In this article, a novel barrier function is introduced to convert the box-constrained convex optimization problem to an unconstrained problem. For each double-sided bounded variable, a single monomial function is added as a barrier…
We provide several applications of the linearization problem of a binary quadratic problem. We propose a new lower bounding strategy, called the linearization-based scheme, that is based on a simple certificate for a quadratic function to…
We address the problem of minimizing a smooth function $f^0(x)$ over a compact set $D$ defined by smooth functional constraints $f^i(x)\leq 0,~ i = 1,\ldots, m$ given noisy value measurements of $f^i(x)$. This problem arises in…
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…
Permutation pattern-avoidance is a central concept of both enumerative and extremal combinatorics. In this paper we study the effect of permutation pattern-avoidance on the complexity of optimization problems. In the context of the dynamic…
Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…
The evolution of the human society raises more and more difficult endeavors. For some of the real-life problems, the computing time-restriction enhances their complexity. The Matrix Bandwidth Minimization Problem (MBMP) seeks for a…
We study an iterative matrix conditioning algorithm due to Osborne (1960). The goal of the algorithm is to convert a square matrix into a balanced matrix where every row and corresponding column have the same norm. The original algorithm…
Regularization-based approaches for injecting constraints in Machine Learning (ML) were introduced to improve a predictive model via expert knowledge. We tackle the issue of finding the right balance between the loss (the accuracy of the…
The primal problem of multinomial likelihood maximization restricted to a convex closed subset of the probability simplex is studied. Contrary to widely held belief, a solution of this problem may assign a positive mass to an outcome with…
This paper focuses on the convergence certificates of the majorized proximal alternating minimization (PAM) method with subspace correction, proposed in \cite{TaoQianPan22} for the column $\ell_{2,0}$-norm regularized factorization model…
Consider the problem of minimizing an expected logarithmic loss over either the probability simplex or the set of quantum density matrices. This problem includes tasks such as solving the Poisson inverse problem, computing the…
We develop a novel stepsize based on \BB method for solving some challenging optimization problems efficiently, named regularized \BB (RBB) stepsize. We indicate that RBB stepsize is the close solution to a $\ell_{2}^{2}$-regularized least…
In this paper, we investigate optimization problems with nonnegative and orthogonal constraints, where any feasible matrix of size $n \times p$ exhibits a sparsity pattern such that each row accommodates at most one nonzero entry. Our…
The classical branch-and-bound algorithm for the integer feasibility problem has exponential worst case complexity. We prove that it is surprisingly efficient on reformulated problems, in which the columns of the constraint matrix are…