Global Solutions to Non-Convex Functional Constrained Problems with Hidden Convexity

• URL: http://arxiv.org/abs/2511.10626v1
• Date: Fri, 14 Nov 2025 02:00:29 GMT
• Title: Global Solutions to Non-Convex Functional Constrained Problems with Hidden Convexity
• Authors: Ilyas Fatkhullin, Niao He, Guanghui Lan, Florian Wolf,
• Abstract summary: We develop algorithms to solve non-provably provably complex problems.<n>First, we establish global last-rate convergence guarantees with complexity $widetildemathcalO(varepsilon-1)$ oracle in nonsmooth space.<n>For problems, we propose a new bundle-level type method based on linearly constrained quadratic subproblems.
• Score: 26.72817687373639
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Constrained non-convex optimization is fundamentally challenging, as global solutions are generally intractable and constraint qualifications may not hold. However, in many applications, including safe policy optimization in control and reinforcement learning, such problems possess hidden convexity, meaning they can be reformulated as convex programs via a nonlinear invertible transformation. Typically such transformations are implicit or unknown, making the direct link with the convex program impossible. On the other hand, (sub-)gradients with respect to the original variables are often accessible or can be easily estimated, which motivates algorithms that operate directly in the original (non-convex) problem space using standard (sub-)gradient oracles. In this work, we develop the first algorithms to provably solve such non-convex problems to global minima. First, using a modified inexact proximal point method, we establish global last-iterate convergence guarantees with $\widetilde{\mathcal{O}}(\varepsilon^{-3})$ oracle complexity in non-smooth setting. For smooth problems, we propose a new bundle-level type method based on linearly constrained quadratic subproblems, improving the oracle complexity to $\widetilde{\mathcal{O}}(\varepsilon^{-1})$. Surprisingly, despite non-convexity, our methodology does not require any constraint qualifications, can handle hidden convex equality constraints, and achieves complexities matching those for solving unconstrained hidden convex optimization.

Related papers

• Nonsmooth Projection-Free Optimization with Functional Constraints [12.20060970177791]
  This paper presents a subgradient-based algorithm for constrained nonsmooth convex computation. Our proposed algorithm can handle nonsmooth problems with general convex functional inequality constraints. Similar performance is observed when deterministic subgradients are replaced with subgradients.
  arXiv  Detail & Related papers  (2023-11-18T23:06:33Z)
• Universal Online Learning with Gradient Variations: A Multi-layer Online Ensemble Approach [57.92727189589498]
  We propose an online convex optimization approach with two different levels of adaptivity. We obtain $mathcalO(log V_T)$, $mathcalO(d log V_T)$ and $hatmathcalO(sqrtV_T)$ regret bounds for strongly convex, exp-concave and convex loss functions.
  arXiv  Detail & Related papers  (2023-07-17T09:55:35Z)
• First-order Methods for Affinely Constrained Composite Non-convex Non-smooth Problems: Lower Complexity Bound and Near-optimal Methods [23.948126336842634]
  We make the first attempt to establish lower complexity bounds of first-order FOMs for solving a composite non-smooth optimization problem. We find that our method and the proposed IPG method are almostimprovable.
  arXiv  Detail & Related papers  (2023-07-14T19:59:18Z)
• A Block Coordinate Descent Method for Nonsmooth Composite Optimization under Orthogonality Constraints [7.9047096855236125]
  We show that textbfOBCD offers stronger optimality than standard critical points.<n>We also demonstrate the non-erg convergence rate of textbfOBCD.
  arXiv  Detail & Related papers  (2023-04-07T13:44:59Z)
• Accelerated First-Order Optimization under Nonlinear Constraints [61.98523595657983]
  We exploit between first-order algorithms for constrained optimization and non-smooth systems to design a new class of accelerated first-order algorithms.<n>An important property of these algorithms is that constraints are expressed in terms of velocities instead of sparse variables.
  arXiv  Detail & Related papers  (2023-02-01T08:50:48Z)
• Oracle Complexity of Single-Loop Switching Subgradient Methods for Non-Smooth Weakly Convex Functional Constrained Optimization [12.84152722535866]
  We consider a non- constrained optimization problem where the objective function is weakly convex or weakly convex. To solve the problem, we consider the subgradient method, which is first-order tuning and easily implement.
  arXiv  Detail & Related papers  (2023-01-30T22:13:14Z)
• A Constrained Optimization Approach to Bilevel Optimization with Multiple Inner Minima [49.320758794766185]
  We propose a new approach, which convert the bilevel problem to an equivalent constrained optimization, and then the primal-dual algorithm can be used to solve the problem. Such an approach enjoys a few advantages including (a) addresses the multiple inner minima challenge; (b) fully first-order efficiency without Jacobian computations.
  arXiv  Detail & Related papers  (2022-03-01T18:20:01Z)
• Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process [56.55075925645864]
  The problem of constrained decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints. A new utilities-dual convex approach is proposed with novel integration of three ingredients: regularized policy, dual regularizer, and Nesterov's gradient descent dual. This is the first demonstration that nonconcave CMDP problems can attain the lower bound of $mathcal O (1/epsilon)$ for all complexity optimization subject to convex constraints.
  arXiv  Detail & Related papers  (2021-10-20T02:57:21Z)
• Oracle Complexity in Nonsmooth Nonconvex Optimization [49.088972349825085]
  It is well-known that given a smooth, bounded-from-below $$stationary points, Oracle-based methods can find smooth approximation of smoothness. In this paper, we prove an inherent trade-off between optimization and smoothing dimension.
  arXiv  Detail & Related papers  (2021-04-14T10:42:45Z)
• Recent Theoretical Advances in Non-Convex Optimization [56.88981258425256]
  Motivated by recent increased interest in analysis of optimization algorithms for non- optimization in deep networks and other problems in data, we give an overview of recent results of theoretical optimization algorithms for non- optimization.
  arXiv  Detail & Related papers  (2020-12-11T08:28:51Z)
• An efficient nonconvex reformulation of stagewise convex optimization problems [21.61123565780424]
  We develop a non reformulation designed to exploit staged structure problems. For neural network verification approach obtains spurious local gaps in only a few steps. It can quickly solve problems faster than both offthe-shelf and specialized solvers.
  arXiv  Detail & Related papers  (2020-10-27T14:30:32Z)
• Conditional gradient methods for stochastically constrained convex minimization [54.53786593679331]
  We propose two novel conditional gradient-based methods for solving structured convex optimization problems. The most important feature of our framework is that only a subset of the constraints is processed at each iteration. Our algorithms rely on variance reduction and smoothing used in conjunction with conditional gradient steps, and are accompanied by rigorous convergence guarantees.
  arXiv  Detail & Related papers  (2020-07-07T21:26:35Z)
• Conditional Gradient Methods for Convex Optimization with General Affine and Nonlinear Constraints [8.643249539674612]
  This paper presents new conditional gradient methods for solving convex optimization problems with general affine and nonlinear constraints. We first present a new constraint extrapolated condition gradient (CoexCG) method that can achieve an $cal O (1/epsilon2)$ iteration complexity for both smooth and structured nonsmooth function constrained convex optimization. We further develop novel variants of CoexCG, namely constraint extrapolated and dual regularized conditional gradient (CoexDurCG) methods, that can achieve similar iteration complexity to CoexCG but allow adaptive selection for algorithmic parameters.
  arXiv  Detail & Related papers  (2020-06-30T23:49:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.