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An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We derive a simple lower bound on the geometric measure of entanglement for mixed quantum states in the case of a general multipartite system. The main ingredient of the presented derivation is the triangle inequality applied to the root…
The geometric measure of entanglement of a pure quantum state is defined to be its distance to the space of product (seperable) states. Given an $n$-partite system composed of subsystems of dimensions $d_1,\ldots, d_n$, an upper bound for…
The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to…
We consider several classes of highly important semidefinite optimization problems that involve both a convex objective function (smooth or nonsmooth) and additional linear or nonlinear smooth and convex constraints, which are ubiquitous in…
Quadratic systems with lossless quadratic terms arise in many applications, including models of atmosphere and incompressible fluid flows. Such systems have a trapping region if all trajectories eventually converge to and stay within a…
We give the first approximation algorithm for mixed packing and covering semidefinite programs (SDPs) with polylogarithmic dependence on width. Mixed packing and covering SDPs constitute a fundamental algorithmic primitive with recent…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
This paper discusses properties of quantum fingerprinting with shared entanglement. Under certain restriction of final measurement, a relation is given between unitary operations of two parties. Then, by reducing to spherical coding…
The entanglement measure for multiqudits is proposed. This measure calculates the partial entanglement distributed by subsystems and the complete entanglement of the total system. This shows that we need to measure the subsystem…
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…
We first show a simple but striking result in bilevel optimization: unconstrained $C^\infty$ smooth bilevel programming is as hard as general extended-real-valued lower semicontinuous minimization. We then proceed to a worst-case analysis…
A variety of large-scale machine learning problems can be cast as instances of constrained submodular maximization. Existing approaches for distributed submodular maximization have a critical drawback: The capacity - number of instances…
We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice ${\bf Z}^n$. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the…
Semidefinite programs (SDPs) are a class of optimisation problems that find application in numerous areas of physics, engineering and mathematics. Semidefinite programming is particularly suited to problems in quantum physics and quantum…
Typical constraints on embedded systems include code size limits, upper bounds on energy consumption and hard or soft deadlines. To meet these requirements, it may be necessary to improve the software by applying various kinds of…
The reachability analysis of weighted pushdown systems is a very powerful technique in verification and analysis of recursive programs. Each transition rule of a weighted pushdown system is associated with an element of a bounded semiring…
We consider the mixed three-qubit bound entangled state defined as the normalized projector on the subspace that is complementary to an Unextendible Product Basis [C. H. Bennett et. al., Phys. Rev. Lett. 82, 5385 (1999)]. Using the fact…
Quantum entanglement between several particles is essential for applications like quantum metrology or quantum cryptography, but it is also central for foundational phenomena like quantum non-locality. This leads to the problem of…
High-dimensional (HD) entanglement promises both enhanced key rates and overcoming obstacles faced by modern-day quantum communication. However, modern convex optimization-based security arguments are limited by computational constraints;…