Novel approximation hierarchy for sparse quadratic programs.
problem Sparse Quadratic Programs with Cardinality Constraints.
method Exploits rank-dominating eigenvectors for min-max optimization over binary variables.
result Efficient screening of nonzero elements with scalable optimization algorithms.
We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same quadratic form, or if the qu…
Abstract perspective on quadratic programming for optimal portfolio allocation.
problem Optimal allocation problems in long portfolio theory.
method Using maximum principles and distinguished boundaries in reproducing kernel Hilbert spaces.
result Support of an optimal distribution lies in a variety intersecting a distinguished boundary.
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are mostly not scalable. In this paper, we develop a method that transforms the quadra…
Paper presents an ADMM-based approach to efficiently integrate quadratic programming layers into neural networks.
problem Integrating quadratic programs into neural networks for optimization.
method An ADMM-based network layer architecture for solving quadratic programs efficiently.
result The ADMM layer is approximately an order of magnitude faster than existing methods for medium scaled problems.
Eigen-decomposition simplifies quadratic programming with equality constraints.
problem Optimizing solutions under linear equality constraints in quadratic programming.
method Eigenvalue decomposition of the quadratic term matrix to project optimal solutions.
result Established a linear mapping between EQP formulations with and without diagonalized Q. Faster algorithms for structured SVMs reduce computation time.
problem Efficiently solving quadratic programming problems with specific structures.
method Designing nearly-linear time algorithms for quadratic programs with low-rank factorizations and few linear constraints.
result First nearly-linear time algorithms for solving quadratic programs with specific structures.
New method solves constrained stochastic optimization problems efficiently.
problem Online statistical inference of constrained stochastic nonlinear optimization problems.
method Stochastic Sequential Quadratic Programming (StoSQP) with iterative sketching solver.
result The rescaled primal-dual sequence converges to a mean-zero Gaussian distribution.
Method solves complex optimization problems with high probability bounds.
problem Nonlinear equality constrained stochastic optimization problems.
method Step-search sequential quadratic programming method.
result High-probability bound on iteration complexity for first-order stationarity.
Novel method solves group synchronization with robust corruption tolerance.
problem Group synchronization with high corruption tolerance.
method Quadratic programming formulation exploiting cycle consistency.
result Global minimum recovers corruption levels under mild conditions.
New method solves nonseparable stochastic control problems.
problem Nonseparable and non-monotonic stochastic control problems.
method Scenario-decomposition solution framework using progressive hedging algorithm.
result Extends reach of stochastic optimal control.
The Slope Conjecture relates a quantum knot invariant, (the degree of the colored Jones polynomial of a knot) with a classical one (boundary slopes of incompressible surfaces in the knot complement). The degree of the colored Jones polynomial can be computed by a suitable (almost tight) state sum and the solution of a …
New method solves optimization problems with stochastic objectives and constraints.
problem Optimization problems with stochastic objectives and deterministic constraints.
method Trust-region interior-point stochastic sequential quadratic programming (TR-IP-SSQP) method.
result Global almost-sure convergence to first-order stationary points under standard assumptions.
We propose a randomized second-order method for optimization known as the Newton Sketch: it is based on performing an approximate Newton step using a randomly projected or sub-sampled Hessian. For self-concordant functions, we prove that the algorithm has super-linear convergence with exponentially high probability, wi…
New algorithm speeds up path computation for optimal models.
problem Finding the exact path of optimal models from a finite set.
method Dynamic programming approach for linear time computation.
result Dynamic programming achieves linear time for breakpoints computation.
In this paper we propose a tractable quadratic programming formulation for calculating the equilibrium term structure of electricity prices. We rely on a theoretical model described in [21], but extend it so that it reflects actually traded electricity contracts, transaction costs and liquidity considerations. Our nume…
Efficiently solves heterogeneous QPs by reducing variables using instance-specific projections.
problem Solving high-dimensional quadratic programming problems efficiently.
method Data-driven framework with a graph neural network generating projections tailored to each QP instance.
result Produces high-quality solutions with reduced computation time, outperforming existing methods.
We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different k-sparse solutions may be present in the feasible set, and the classical l1 approach may be unsuccessfu…
Neural network discovers exact solutions to QP with linear constraints.
problem Discovering exact solutions to Quadratic Programs (QP) with linear constraints using neural networks.
method Proposes a neural network modeling approach that analytically derives model parameters from problem coefficients, ensuring closed-form solutions without training.
result The closed-form NN model produces exact solutions for every critical region of the QP solution function, outperforming DNNs and commercial solvers in terms of optimality and feasibility.
Paper approximates Kelly betting for wealth growth.
problem Optimizing wealth growth in Kelly betting.
method Taylor-based approximation for quadratic programming.
result Closed-form approximate solution with interesting properties.
New algorithm tackles stochastic optimization with inequality constraints.
problem Stochastic optimization with inequality constraints in various applications.
method Active-set stochastic sequential quadratic programming (StoSQP) with a differentiable exact augmented Lagrangian.
result Global convergence for any initialization, KKT residuals converge to zero almost surely.
Semidefinite programs (SDP) are important in learning and combinatorial optimization with numerous applications. In pursuit of low-rank solutions and low complexity algorithms, we consider the Burer--Monteiro factorization approach for solving SDPs. We show that all approximate local optima are global optima for the pe…
We consider the problem of estimating the phases of K mixed complex signals from a multichannel observation, when the mixing matrix and signal magnitudes are known. This problem can be cast as a non-convex quadratically constrained quadratic program which is known to be NP-hard in general. We propose three approaches t…
The paper shows how label noise in training can lead to solutions that solve a Lasso program.
problem Understanding the implicit bias of training algorithms in overparametrised models.
method Analyzing the continuous time version of the training dynamics of a quadratically parametrised model.
result The stochastic flow implicitly solves a Lasso program, providing convergence guarantees and support recovery conditions.
A new portfolio optimization model minimizes maximum drawdown, offering faster and more robust solutions.
problem Optimizing portfolios during financial distress, especially during crises.
method Linearization of Markowitz model based on maximum drawdown, with a Mixed-Integer Linear Programming variation.
result 200 times faster solving time with a more profitable and robust solution.
To estimate the conditional probability functions based on the direct problem setting, V-matrix based method was proposed. We construct V-matrix based constrained quadratic programming problems for which the inequality constraints are inconsistent. In particular, we would like to present that the constrained quadratic …
Reconstructing polytopes with fixed facet directions from support function evaluations.
problem Reconstructing polytopes with known facet directions from limited data.
method Least-squares estimate via convex quadratic program, combinatorial characterization for uniqueness, algorithm convergence.
result The least-squares estimate for a fixed simplicial normal fan is a convex quadratic program, and the solution is unique under certain conditions.
This research optimizes Andrews plots for better visual clarity in high-dimensional data.
problem Visualizing high-dimensional datasets with clarity and aesthetics.
method Developed a method to add spectral smoothing to Andrews plots to reduce visual clutter.
result Optimal spatial-spectral smoothing leads to more aesthetically pleasing and clutter-free visualizations.
This paper speeds up OCSSVM training using SMO.
problem Training One-Class Slab SVMs is slow.
method Uses updated SMO to divide large problems into smaller, analytically solvable subproblems.
result Training OCSSVMs scales better with large datasets.
New algorithm solves stochastic optimization problems with unknown gradients.
problem Solving nonlinear optimization problems with stochastic objectives and deterministic constraints.
method Adaptive SQP with differentiable exact augmented Lagrangian and stochastic line search.
result Global convergence established for both non-adaptive and adaptive SQP methods.
New method solves stochastic optimization problems with random models.
problem Optimizing stochastic objectives with deterministic constraints.
method Trust-Region Sequential Quadratic Programming with random model.
result Global convergence guarantees for first- and second-order stationary points.
A novel formulation and training procedure for full Boltzmann machines in terms of a mixed binary quadratic feasibility problem is given. As a proof of concept, the theory is analytically and numerically tested on XOR patterns.
Integrates prediction models into portfolio optimization for better asset allocation.
problem Traditional portfolio optimization ignores prediction models, leading to suboptimal decisions.
method Developed a framework that combines regression prediction with mean-variance optimization, providing analytical solutions and neural-network-based optimization for inequality constraints.
result Demonstrated through simulations that integrating prediction models improves portfolio performance.
A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center of their own classes, while maximimizing the distance between class centers. We …
Develops an online method for solving constrained optimization problems with debiasing techniques.
problem Online inference of solutions to constrained optimization problems with equality and inequality constraints.
method Stochastic Sequential Quadratic Programming (SSQP) with momentum debiasing.
result Achieves global almost-sure convergence and local asymptotic normality with optimal primal-dual limiting covariance.
We propose an SDP relaxation for the Gromov-Wasserstein distance, providing globally optimal solutions.
problem Matching objects between incomparable spaces using the Gromov-Wasserstein distance.
method Semi-definite programming (SDP) relaxation of the GW distance.
result The SDP relaxation provides globally optimal solutions for the GW distance in some instances.
In this paper we consider l0 regularized convex cone programming problems. In particular, we first propose an iterative hard thresholding (IHT) method and its variant for solving l0 regularized box constrained convex programming. We show that the sequence generated by these methods converges to a local minimizer.…
Extends trading framework to incorporate real-world constraints.
problem Trading strategies in multi-player non-cooperative games with constraints.
method Re-framed as quadratic programming problem, constraints readily incorporated.
result Two-trader equilibria calculated dynamically.
We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the relevant variables. Our approach is a two-stage quadratic programming method that…
Simplified approach to portfolio risk management and hedging in practice.
problem Challenges in applying academic portfolio risk management and hedging in real-world business settings.
method A straightforward approach using convex optimization and quadratic programming.
result Demonstrates how to solve portfolio risk management and hedging problems with CVXOPT.
Improves scalability of Bayesian optimization for combinatorial spaces.
problem Optimizing expensive functions over large combinatorial spaces.
method Parametrized Submodular Relaxation (PSR) to solve AFO problems for BOCS.
result Significant improvements in scalability and accuracy for BOCS model.
Motivated by electricity consumption metering, we extend existing nonnegative matrix factorization (NMF) algorithms to use linear measurements as observations, instead of matrix entries. The objective is to estimate multiple time series at a fine temporal scale from temporal aggregates measured on each individual serie…
Paper proposes government indemnification for AI risks to solve judgment-proof problem.
problem Uninsurable risks from AI, especially existential risks, create a judgment-proof problem.
method A government-provided, mandatory indemnification program using risk-priced fees and Bayesian Truth Serum.
result The approach better leverages private information and signals risk mitigation efforts.
Proposes a new algorithm for solving optimization problems with stochastic objectives and equality constraints.
problem Optimization problems with stochastic objectives and deterministic equality constraints.
method Trust-region stochastic sequential quadratic programming (TR-StoSQP) with adaptive relaxation techniques.
result Established a global almost sure convergence guarantee for TR-StoSQP.
Paper develops a TR-SSQP method for noisy optimization with heavy-tailed noise.
problem Optimization problems with stochastic objectives and heavy-tailed noise.
method Trust-Region Stochastic Sequential Quadratic Programming (TR-SSQP) method.
result Achieves high-probability first-order and second-order stationarity bounds for heavy-tailed noise.
Paper proposes a novel optimization method for disaggregating smart meter data.
problem Energy disaggregation, inferring appliance-specific energy consumption from aggregate meter data.
method Two-stage optimization approach: first phase uses mixed integer programming, second phase binary quadratic optimization with penalty terms and appliance constraints.
result Proposed method successfully reconstructs appliance signatures, overcoming previous optimization-based methods' limitations.
Paper studies vertex correspondence recovery in correlated graphs with node features.
problem Recovering hidden vertex correspondence between two correlated graphs with observed edge weights and node features.
method Introduced featured correlated Gaussian Wigner model and proposed QPAlign algorithm for quadratic programming relaxation.
result Characterized optimal information-theoretic thresholds for exact and partial recovery of latent mapping.
Study of energy conservation in fourth-order gravity theories.
problem Conservation principles in fourth-order gravitational theories.
method Detailed analysis of energy concepts, focusing on quadratic Lagrangian and solutions.
result Presentation of positive energy theorems in restricted situations.