Related papers: A Generalized $\ell_1$-Merit Function SQP Method U…
This paper mainly concerns with the primal superlinear convergence of the quasi-Newton sequential quadratic programming (SQP) method for piecewise linear-quadratic composite optimization problems. We show that the latter primal superlinear…
We consider the nonlinear optimization problem with least $\ell_1$-norm measure of constraint violations and introduce the concepts of the D-stationary point, the DL-stationary point and the DZ-stationary point with the help of exact…
We propose a novel stochastic approximation algorithm, termed PMQSopt, for solving weakly convex stochastic optimization problems involving expectation-valued functions. The algorithm is constructed by integrating the proximal method of…
We propose a new family of inexact sequential quadratic approximation (SQA) methods, which we call the inexact regularized proximal Newton ($\textsf{IRPN}$) method, for minimizing the sum of two closed proper convex functions, one of which…
In this paper, we present a stabilized sequential quadratic semidefinite programming (SQSDP) method for nonlinear semidefinite programming (NSDP) problems and prove its local convergence. The stabilized SQSDP method is originally developed…
Penalty methods are a well known class of algorithms for constrained optimization. They transform a constrained problem into a sequence of unconstrained \emph{penalized} problems in the hope that approximate solutions of the latter converge…
We present an approach called Q-probing to adapt a pre-trained language model to maximize a task-specific reward function. At a high level, Q-probing sits between heavier approaches such as finetuning and lighter approaches such as few shot…
We study reinforcement learning with linear function approximation and finite-memory approximations for partially observed Markov decision processes (POMDPs). We first present an algorithm for the value evaluation of finite-memory feedback…
We consider the problem of computing the q->p norm of a matrix A, which is defined for p,q \ge 1, as |A|_{q->p} = max_{x !=0 } |Ax|_p / |x|_q. This is in general a non-convex optimization problem, and is a natural generalization of the…
Motivated by the result that an `approximate' evaluation of the Jones polynomial of a braid at a $5^{th}$ root of unity can be used to simulate the quantum part of any algorithm in the quantum complexity class BQP, and results relating BQP…
Convex quadratic programs (QPs) constitute a fundamental computational primitive across diverse domains including financial optimization, control systems, and machine learning. The alternating direction method of multipliers (ADMM) has…
We study a Q learning algorithm for continuous time stochastic control problems. The proposed algorithm uses the sampled state process by discretizing the state and control action spaces under piece-wise constant control processes. We show…
This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…
A natural and important generalization of submodularity -- $k$-submodularity -- applies to set functions with $k$ arguments and appears in a broad range of applications, such as infrastructure design, machine learning, and healthcare. In…
Quadratically constrained quadratic programming (QCQP) has long been recognized as a computationally challenging problem, particularly in large-scale or high-dimensional settings where solving it directly becomes intractable. The complexity…
We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide…
This paper investigates the problem of efficient constrained global optimization of hybrid models that are a composition of a known white-box function and an expensive multi-output black-box function subject to noisy observations, which…
We recently introduced a scale of kernel-based greedy schemes for approximating the solutions of elliptic boundary value problems. The procedure is based on a generalized interpolation framework in reproducing kernel Hilbert spaces and was…
Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed randomized…
This paper reveals that a common and central role, played in many error bound (EB) conditions and a variety of gradient-type methods, is a residual measure operator. On one hand, by linking this operator with other optimality measures, we…